If you bought your snorkel gear in one of those "all in one" bags at Walmart, then it will probable not hold up well below 20 feet.
If you bought realitively moderately priced mask, fins and snorkel at a SCUBA shop or sporting goods store it is possably good enough to get you through a beganning SCUBA class.
The only real difference in the gear for snorkeling is that teh fins will usually be the full foot pocket type that fit like a slip on shoe. They are only good for really warm water because you can not get a neoprene booty into the fin. Also good snorkel fins are very long in compairison to SCUBA fins. They are designed for surface swimming and strong drive to surfce dive. Long fins don't work well when you SCUBA dive because it is difficult to turn, sit on the bottom for a class and SCUBA divers don't really do strong kicking because all the gear you will have on creates a lot of drag.
Once you get started with the class you will figure out if your snorkel gear is the right fit for the task or not, before you really do any open ocean dives.