I love red snapper, I'd like to think I can tell the difference between that and Tilapia (or any other fish). I guess it depends on how you eat your fish. In general I usually buy whole red snapper and can obviously see what it is, it is also quite bonny than most fish.
Unfortunately most American fish preparation methods (deep fry, heavy saucing) basically destroys the fish flavor so people may not develop the ability to differentiate.