There are many varieties of peaches in the world today. But since all the commercially available peaches are more or less delicious, consumers only need to know one thing about any peach they might buy: Is it freestone or cling?
The names explain themselves. With freestone peaches, when sliced, the fruit easily separates from the pit, or the stone. Cling (sometimes called clingstone) can be sliced around the pit, but when you try to gently twist the fruit, you end up mangling it till it's mush. A very sad and sticky situation.
Unless your superpower is the ability to identify different varieties of fruit on sight (which would make you pretty cool, and/or a farmer), it's difficult to know whether a given peach is freestone or cling. Cling peaches often are reserved for canning and jamming, but the whole fruit makes it to market, too. Generally speaking, cling peaches are harvested earlier in the season, with freestones getting ripe later in the summer.
There are some peaches marketed as “semi-cling,” but those are a lie. Do not expect to get clean slices from those peaches.
There is no difference in taste between the two types of peaches, just ease of use. Either option is great if you're eating out of hand. But if you have loftier goals, check the signage at the supermarket (they sometimes will have this information listed) or ask at the farmers market. In the process, maybe you'll figure out which peach varieties are your favorites, which would make you a superhero.