Cryptographers seem to have a thing for misleading names. A big one is "provable security" which really means "is at least as hard as another more old and famous problem that we are all guessing is hard to solve efficiently." In any case "provable security" alone is often too difficult to prove so more assumptions are added to make the proof go through. Saying you've obtained provable security under some assumptions doesn't sound very good though, so the assumptions are called "models" instead.