Dragons don't NEED anything to be what they are. They can be wingless for all I care. (Glaurung was wingless.) Oriental dragons are depicted without wings, and sometimes limbless as well. To me, the requirements for dragons are more fluid. As long as they are great, fire-breathing serpents, I'm fine with anything.
Smaug looked every bit the dragon in the movie. He had forelegs and hind legs, and the wings just happened to be attached to the former.
And I've always thought wyverns were dragon-like creatures with a barbed tail like a scorpion.