American Association of Snowboard Instructors used to say there were 3 levels of carving (keep in mind there are other types of turns as well), but it has been a while since I was teaching so correct me if i am wrong.
1) Carving - having the body cross over the board extended and maintaining the body extended throughout the turn. This is often the most common seen, slower transition.
2) Dynamic Carved Turn - looks like pumping in the turn. This type of turn the rider is extended in the transition, sinks the body into the turn, then pumps out to an extended position before the end of the turn, and is extended during the transition.
3) Advanced Dynamic Carved Turn - rider is compressed during transition, uncompressed to the apex of the turn, then as the turn completes re-compresses to complete the turn and transition to the other edge. In this type of turn a riders hip maintain the same height off the snow, and the board appears to move like a pendulum under the rider.
Hope that helps to provide some information.