No, they aren't the same thing, although what you got might be OK. Basically, stabilizer includes formaldehyde, which is a necessary preservative for older C-41 emulsions. ("Older" being designed by Kodak more than, at a guess, 5 or 10 years ago.) Final rinse lacks the formaldehyde and includes some other, more benign, anti-fungal agent. If you use final rinse on an older emulsion, dye stability might suffer. If you use final rinse on a newer emulsion, everything should be OK. I believe that somewhere on Kodak's labyrinthine Web site there's a detailed specification of what Kodak films requires stabilizer and what ones work OK with final rinse. Basically all modern Kodak, and I believe Fuji, films are fine with final rinse. If you've got older films, though, or films from other manufacturers, you might need stabilizer to ensure stability beyond a few years.
FWIW, the same thing happened to me recently on an order from Adorama -- the Web page (and invoice) specifies stabilizer, but the bottle says final rinse. The Kodak part numbers match, so it seems that Adorama's Web site description is messed up.