I usually cook vegetarian dishes because it's easier for me although I'm a huge carnivore. I'm taking a stab at this steak sandwich recipe which calls for "fillet of beef". What does that mean? Which cut (chuck roast, london broil, etc...) can I get? Surely Ina Garten does not mean fillet mignon?
I believe it's another name for the tenderloin. http://www.recipes4us.co.uk/Beef%20Cuts.htm
Also, if you check out this other fillet of beef recipe from the same show: http://www.foodnetwork.com/recipes/ina-garten/fillet-of-beef-recipe/index.html You can see a much better picture of the meat. That one is clearly a tenderloin.
So The Fillet Mignon is part of that technically...
A fillet is steak cut from the tenderloin. If you cut the tenderloin into "medallions" it becomes a fillet (better when wrapped with bacon...but isn't everything) and is ready to be grilled or broiled. If you leave the tenderloin in tact, then it is a 'tenderloin roast' suitable for use in a beef wellington.
For a good lesson on using tenderloin, see Alton Brown's "Tender is the Loin"
A filet is any boneless cut of meat (it's a generic term); usually one of higher quality. You could have a filet, for instance, off the strip loin (a manhattan filet). Typically, however, when someone says "filet", they're referring to the "filet mignon" (literally "small boneless cut of meat"), which is a cut from the front end of a beef tenderloin, a sub-primal cut that crosses the sirloin and short loin.