Nectarines are, botanically speaking, a variety of peach. They are so closely related that nectarines often appear on the branches of peach trees.
Some people claim that nectarines have a slightly lighter flavor, and peaches tend to be a bit more deeply flavored. Technically the only difference is the name and the lack of peach fuzz on the smooth skin of nectarines. Because they lack fuzz, some people prefer to eat them out-of-hand, and the skin can be left on when baking.