This gets just about beat to death time after time - and research will get you different answers.
For example, here's the wikipedia definition of tenderloin, the keys beingits name, as well as thelocation of the muscle, which is internal.
Beef tenderloin, or
eye fillet (
New Zealand and
Australia), is cut from the
loin of a steer or heifer. As with all
quadrupeds, the tenderloin refers to the
Psoas major muscle along the central spine portion, which more or less hangs between the shoulder blade and hip socket
There seems to be great variation as to local definitions concerning these cuts of meat. My take is that the tenderloin is this relatively small internal muscle, being the very best as Fordman stated, while the backstrap is theconsiderably larger(also very good cut) muscle running along the spine between the backbone and the hide. The latter lends itself to delicious butterfly chops and I tend to cut them about 3/4 inch thick. Any good meat marinade will enhance these chops, but I bbq the tenderloins without any doctoring.
BTW, if you check out a T-bone steak in a store, there's 2 portions of meat on opposite sides of the bone. The smaller bit is the tenderloin and the larger part is backstrap.
Regardless, I'm sure you'll enjoy that doe immensely.