From the research of historical records either term is correct. For example, in a Website called Links: WW 1 Aviation the following were listed:

Note that the USAF Museum uses the term "Escadrille Lafayette." Next there is a report in the Lafayette Escadrille D'Arizona website:

The original Escadrille began service with the Nieuport 11, then the latest French single-seat fighter. Its upper wing spanned 24' 6', it had a gross weight of 1100 pounds and was propelled aloft by a nine-cylinder, 80hp LeRhone rotary engine. On 30 October, 1916, the first Nieuport 17's arrived. They were slightly larger, with IlOhp rotary engines. Eventually the Nieuports were replaced by more modem types, and today the Escadrille, still an active unit of the French Air Force, flies Mirage 2000 supersonic jet fighters. But it all started here! Today's Escadrille Lafayette 'd Arizona flies 87% scale Nieuport 17 replicas powered by 55-75hp Volkswagen engines. These aircraft are made of aluminum tubing covered with fabric. They are very light but strong. Empty weight is around 450 1bs. The aircraft cruise at 70mph, and stall at 35mph. Although the engines are much more modern than the originals, the performance and handling characteristics are very similar to their 1916 predecessors. We have made a few concessions to modern times for safety's sake: Brakes, steerable tailwheels, battery powered starters, and radios top the list. These and other changes allow us to fly from paved runways and perform reliably and consistently in modern formation flight in practice and at airshows.The members of the original Lafayette Escadrille came from all over the United Stated and represented all walks of life. The Escadrille Lafayette d 'Arizona has that in common with them.

The term "Lafayette Escadrille" is used in the above report. Next, in the Ayer Company Publisher ( http://www.scry.com/ayer/) catalog this book is described:

A Narrative of Air Fighting in France James Norman Hall had no professional work experiences to prepare him for his activities during World War I. He worked as an investigator for the Massachusetts Society for the Prevention of Cruelty to Children, and then sailed to England in 1914 with the intention of writing poetry. The second day after England entered World War I, Hall joined a foreign brigade in the British Army and was transferred into the Air Force in December 1914. After months of training he became a member of the Lafayette Escadrille. He flew in earnest in the 1915 Champagne offensive, fought at Verdun and along the Somme, and was sent to Russia and Rumania. He flew on the Eastern Front and, among many other exploits, attempted to bomb the Kaiser at Sofia. Then he returned to Petrograd and because of the Revolution was forced to depart via Siberia. High Adventure is his story of the formation the Escadrille, French squadron N. 124. "Especially interesting are his activities on the Russian front, and the intimate glimpses of other famous aviators."

Note that the term "Lafayette Escadrille" is also used in the above book review. But in the World War 1 History Gallery Website http://www.wpafb.af.mil/museum/history/ww1/ea.htmwe find this:

Early in World War I, various Americans, sympathetic to the Allied cause, offered their service to France as ambulance drivers, while other of their countrymen fought in the trenches as members of the French Foreign Legion. A handful of these men were successful in transferring to the French Aviation Service prior to the end of 1915, where they were joined by several Americans who enlisted direct from civilian status. A number of these men suggested that France send to the Front a squadron composed of American rather than French pilots. After months of deliberation by the French Government, the Escadrille Americaine, designated N. 124, was formed and on April 20, 1916, it was placed on front-line duty at Luxeuil-les-Bains near Switzerland.

The Escadrille Americaine was commanded by a Frenchman, Captain Georges Thenault, and initially had seven Americans assigned as pilots -- Norman Prince, Victor Chapman, Kiffin Rockwell, James McConnell, William Thaw, Elliot Cowdin, and Bert Hall. During the succeeding twenty months the unit served on the Front, it had an additional thirty-one Americans assigned as pilots, including such legendary figures as Raoul Lufbery and Charles Dolan.

The Escadrille Americaine flew its first mission on May 13, 1916. Five days later Rockwell scored the initial victory for the unit by shooting down a German L.V.G. reconnaissance airplane. On June 23, 1916, Chapman was shot down about 10 miles north of Verdun, thus becoming the first Escadrille Americaine pilot to lose his life while engaging the enemy. The unit continued in combat in succeeding months, and as its fame grew, the German Government protested to the U.S. Government concerning the use of the "Americaine" in the title, since the U.S.A. was still neutral at that time. As a result, France changed the name to Escadrille Lafayette in December 1916.

A little more than a decade after the Wright brothers' historic flight at Kittyhawk, the demands of war transformed the airplane into a weapon of death. Made of wood, canvas and wire, these early fighters took to the air filled with gasoline, ammunition and the likelihood that too steep a dive would rip the wings to shreds. It is no wonder that the pilots of these flimsy fliers measured their life expectancy in weeks. These early pioneers of the air did not have the luxury of a parachute. Just strapping oneself into the cockpit and taking to the air was an act of bravery. Careening into a mid-air duel-to-the-death with an enemy opponent required a special courage.

Raoul Lufbery had this special courage. His flying career began in 1911 when he became mechanic for French pilot Marc Pourpe. The pair barnstormed their way through China, Japan, India, and Egypt finally landing in Paris just as war broke. Porpe joined the French Air Service while Lufbery tagged along as his mechanic. To avenge Porpe’s death at the end of 1914, Lufbery applied for pilot training and earned his wings. He joined other American pilots in the Lafayette Escadrille and scored his first kill in August 1916. By the end of 1917, Lufbery was a leading ace with 17 official kills.

With America in the war, the pilots of the Lafayette Escadrille were absorbed into the American Air Service where their valuable experience was used to train the fledgling pilots. Lufbery was assigned to the 94th Aero Squadron as a teacher and advisor. Lufbery said he never wanted to be burned -- so in his final mission his Nieuport was shot up in a dogfight and was heading down. He jumped out at 2000 feet (without a parachute since they were forbidden).

Note that the term "Lafayette Escadrille" is also used in the above excerpt. There is a movie about the Lafayette Escadrille. It is purportedly about World War 1, Nieuports and the Lafayette Escadrille The movie is not all it was "cracked up to be" as can be seen in this SYNOPSIS AND REVIEW.

Two other productions that included Nieuports and possibly the Lafayette Escadrille recently came to light: One is called "Flying Coffins" and it appeared on television during the last week of August, 1998. The other is called Four Years of Thunder and is available on videotape from the Wingspan Store (which was at http://www.wingspantv.com/wingspan/store.htm  but currently is not available at that URL) Here is a synopsis of Four Years of Thunder:

(US$59.95 + S/H) (4 tapes, 60 mins. each) Toll-free phone number: 1-800-946-4772 (9:00 AM - 5:00 PM EST) or 1-888-572-8916 (after hours or on weekends).

"Four Years of Thunder is the most comprehensive depiction of World War I aerial combat ever done. Much of its footage has never been seen before; and there are many surprises including an authentic cinematic sequence of a German fighter shooting down a French aircraft. This valuable and interesting film greatly contributes to an understanding of aviation's most legendary era."

- Howard G. Fisher Director, League of W.W.I Aviation Historians

Tim Stotts, on the Nieuport Builders Mail List, says of this video: "For anyone serious about the Lafayette Escadrille the only real movie footage I'm aware of was shot of this squadron in May or June 1916 when they first took possesion of their trusty Nieuport 11's. Nearly all of the footage is taxiing and take off stuff but it's interesting to me because it's the real thing."

You may be able to get a video of this silent classic on eBay.  It won an Academy Award for Best Pictures (the first film to get one). According to a review "The aerial battle sequences which abound throughout the film still rank among the best in motion picture history."

My own opinion: Interesting, not really the greatest aerial sequences compared with the movie "The Red Baron." I obtained my copy on eBay -- around US $10.00.

Extremely well done. I did not realize how much film (though silent) was shot in World War I by both sides. Shows stills and silent film of Allied and German aces. Interviews still living World War I pilots from both sides. Gives a detailed biography of Baron Manfred Von Richthofen mostly through actual film clips and stills of the Baron.

It does show one Nieuport 11 -- from other research I found that the only Nieuport 11 clips seem to be of the Nieuport being propped and perhaps taking off. This film shows the Nieuport 11 being propped. Video does show balloons and planes going down and also some excerpts of video of the New York group (the Old Rhinebeck Aerodrome) who owns full-size replicas of the early planes.

The video box states: "Included is WWI footage, dogfights, crashes, and the Red Baron's last flight and the controversy surrounding his death. It's all here, a source of first hand information of his story and the story of his squadron." Note that it shows film clips of Allied back-seat occupants dropping little bombs and well as using the camera (the original mission of World War I pilots -- as observers, like the American War Between the States balloonists).

I obtained my copy on eBay -- around US $10.00.

Red Baron (the original) is aimed for DOS machines. It will work in a DOS window in Windows 95 & 98 but only if you have enough conventional memory available -- may be best run using a separate boot disk (true for many DOS games).

It has rudimentary graphics (for nowadays) but works well. Has sound and you can choose your aircraft (and side!) as well as your enemy.

Red Baron II comes on CD and works with Windows 95 and 98.  You can pick the Nieuport 11 as your aircraft. Nice graphics although sometimes the fields are just a mosaic of squares and rectangles. I thought that you needed to have certain joysticks to make it work but hidden in the manual was the "secret configuration" entrance -- you make a menu choice to just fly and go into a screen where you are flying then right click your mouse -- you can set up many joystick, joypad and rudder pedal combinations by brand name or just generic. I obtained this game on eBay for US $10 plus shipping.

Flying Corps Gold is a game from Rowan Software in England and published by Empire Interactive. It tries (and does succeed for the most part) to be historically accurate with the WWI environment and with the aircraft. There are seven flyable aircraft in this game, the Nieuport 28, Spad XIII, Fokker Triplane, Albatros DIII, Sopwith Camel, Fokker DVIII and an SE5. From the cockpit, the aircraft all look alike in terms of instrumentation. The differences become evident as you glance around in flight and discover each airplane provides a different view of the surroundings.

I did not like the game -- too clunky and instrument panels looked the same.  Difficult to install and run on a Win 98 machine, even with the 1998 patches. To see other reviews on it click on the following:

Bad Review: http://www.magma.ca/~bornaism/FCrev.htm
Good Review: http://www.combatsim.com/archive/htm/htm_arc2/fcgold2.htm

Hunt for the Red Baron (now called Master of the Skies the Red Ace) Get behind the controls of a WW1 fighter plane and take to the skies in Fiendish Games' dogfighting extravaganza - Hunt for the Red Baron. Travel to the green fields of France, hot sands of Africa and the desolate  setting of a war-torn Belgium, as you take part in 25 unique, action-packed missions. Use your machine guns, rockets and bombs to eliminate enemy fighters  and take out key ground targets. Fly four different fighter planes, each with their own feel and handling  based on the actual planes themselves.

                  System requirements:
                  Pentium II 233 mhz - 32MB RAM (will work on 200 mhz machine)
                  File Name: baron-demo-beta.exe
                  Download file Size: 14.7mb
http://www.fiendishgames.com/brands/baron/baron1/game/html/baron_home.htm

In November, 2000, Fiendish Games was bought out by Small Rockets http://www.smallrockets.com/

Hunt for the Red Baron now called  Master of the Skies -- the Red Ace
Download and install the demo version of The Red Ace. Play three levels for FREE!
                                Master of the Skies: The Red Ace
                                Requires: Windows 95/98, Pentium II 233, 4Mb 3D Accelerator, 32Mb Ram, Sound card
                                File size: 14.7Mb  - takes 45.9 Mins on a 56k modem.

WEBMASTER'S OPINION:
Full price $14.99 though demo is fully usable, just has fewer planes and options. To update you just use the online ordering form and you get a code through e-mail. Putting in that code makes your demo a fully functioning game.
I've found it easy to install and fun to play, though not as complete as Red Baron II (no Nieuport 11s).

at ROCKETDOWNLOAD.COM

Reviewers said: Hunt for the Red Baron features nicely developed 3D-style
                      graphics that immerse you in the action. This is a highly
                      enjoyable game, especially if you're not into sophisticated flight
                      simulators. It requires a 3D accelerator card and DirectX drivers.

http://www.rocketdownload.com/Details/Arca/barondemo.htm

This machine was the personal aircraft of Sergeant Raoul Lufbery of the famous Escadrille Lafayette, a French fighter squadron composed of U.S. pilots, during 1916. Lufbery was raised in France, but held U.S. citizenship and rose to become one of the Escadrille Lafayette's best pilots. When the United States entered the war, Lufbery transfered into the U.S. Air Service with the rank of major. He commanded the U.S. 94th Aero Squadron until his death on May 19, 1918. In his last command, he served as a mentor to both Eddie Rickenbacker and Reed Chambers. Lufbery is credited with 17 combat victories, third-highest (after Rickenbacker and Luke) of any American pilot during the war.Data on Lufbery's Nieuport is taken from a drawing of a similar Nieuport by James Goulding, reproduced in Alan Clark's Aces High (New York, G. P. Putnam's Sons, 1973). The "Indian head" squadron insignia was scanned directly from that illustration and colored. Lufbery's plane is shown in a photograph re-produced in Aaron Norman's The Great Air War (New York, Macmillan, 1968). Lufbery's face is scanned from a photograph reproduced in that same work. Both images are credited U.S. Air Force. A third photograph, also credited to the U.S. Air Force, and showing Nieuport 17s of the Escadrille Lafayette on the flight line during the Battle of the Somme, appears in David C. Cooke's Sky Battle: 1914-1918 (New York: W. W. Norton, 1970). This aircraft's serial number was provided by AviBuff@aol.com, who responded quickly and with documentation to an urgent and disjointed Usenet plea for assistance. Thanks.

Special thanks to John J. Cooper (cooperj@nortel.ca) of Ottawa, Canada, for providing the oustanding FSFS model upon which this is based. John is one of the best Flight Shop designers around. He is *the* best when it comes to recreating aircraft with natural metal finishes. He has done a series of Canadian military aircraft from the early 1960s -- look for them, and you'll see what I mean.

Freeware. No warranty.

The Flight Shop Aerodrome whose Internet link is no longer working but you can get the file at The Internet Flight Simulation Archive at IUP : http://compsimgames.miningco.com/msubiup-n.htm as the file N17.ZIP

This Flight Simulator  file uses the "Escadrille Lafayette" phrase.

For those interested in reading in-depth history, here are two accounts using first-person narratives of the Escadrille Lafayette Americaine: They are quite lengthy but may be interesting to some.

From American Volunteer Airmen  by James R. McConnel. Quite lengthy, but divided into five sections.

From Notable American Volunteers of the Great War   by Alan Albright. Not as lengthy but more scholarly -- has 28 (count them) footnotes!

Perhaps the best book on the pilots of the Escadrille Lafayette (and the book uses and explains both manners of writing the name) is Lafayette Escadrille Pilot Biographies. It tells who the real members are (and many who claim they are, aren't! -- there are really only 38 Americans who served ). It has a biography of each member of the Escadrille Lafayette with numerous photos. The book has much detail about the Escadrille Lafayette.

I obtained my copy at Amazon.com.

The phrase "Lafayette Escadrille" is only the Americanized version of the French phrase "Escadrille Lafayette" since in English we place the adjectives before the nouns, unlike the French. So, in keeping with the original version -- the French version, our group is called