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.
"Fillet" is any cut of boneless meat.
It may be spelled "filet" (single "l"), but this spelling varient may imply French cuisine or a specific cut of meat.
"Filet of beef" aka "filet mignon" is cut from the tenderloin.