More likely just plain mozzarella. In most restaurants, you're likely getting a factory pre-made frozen and reheated product from a box - certainly that was the case at the chain pizza place I worked at in highschool. "Stuffed crust" pizza was made with string cheese (at least at the time), though. I've seen blocks of mozzarella chopped up at a fair to fry, but no idea whether that's what everyone does. The "stringiness" of melted mozzarella (as on a pizza or in a fried stick) actually mostly depends on the freshness, or so I've been told.

Maybe not in restaurants, but just frying up some string cheese is indeed the easiest way to make your own at home. Tip: freeze them on a cookie sheet after (double-)breading them, that way they won't melt as soon as you throw them in the fryer.