In my setting, I've split dragons into two groups: Drakes, and true Dragons. Drakes are your big beasty; dangerous, need to slay them, the basic. They're intelligent, but not hyper so. They don't have a culture. Just big, dominant monsters.
Dragons, on the other hand, are akin to gods. But, that doesn't mean omnipotent gods, as my setting is animistic and has tons of lesser spirits that are seen as gods. Dragons are just one kind of such a god.