That's definitely a dolphin. I've seen dolphins do that near the beach in Florida. The first time I saw that happen, it scared the bejeesus out of me. However, sharks do come into the surf, too. There was video of a South African surfer who got himself bit on the hand a couple of years ago. He got away, but he got bit while he was going over a swell, and there were a couple more sharks making their way in. This guy was lucky to get away with his hand and his life!
JediMAC speaks the truth about the New Jersey case. It was in 1916 in the area of Matawan, NJ. The waterway where it happened it now known as the Shark River. The shark(s) in question made their way pretty far from shore. Check out the story on those attacks
here.