A filet mignon is cut from the tenderloin, which lies in the middle of the animal's back. Because the muscles in this area are not overly exerted, their tendons do not toughen -- and that's why a tenderloin is so tender. Strictly speaking, filet mignon comes from the tail end (the smaller end) of the tenderloin; it is generally only 1 to 2 inches in diameter. However, you can use beef filet mignon and beef tenderloin steaks (cut from other parts of the tenderloin) interchangeably. Both are usually cut 1 to 2 inches thick, though beef tenderloin steaks tend to be larger in diameter (2 to 3 inches).
Note that what you gain in tenderness, you lose a bit in flavor -- the lack of marbling, fat, and bone diminishes the beefy taste of these cuts. That's why tenderloin steaks are often served with sauces, toppings, or pan juices. Steak houses also often serve beef tenderloin steaks wrapped in bacon to keep them moist while cooking and add meaty flavor.