A slide-in range is less deep than a free-standing range and is made to overlap the countertop for a more built-in look. You also need a strip of countertop behind the range as well. By the way, the pro-style free-standing ranges (e.g. Wolf, DCS, Bluestar, etc.) don't have the backsplash in the back either. Generally there are fewer models of slide-in ranges with fewer features and they're more expensive than free-standing ranges - you pay a premium for the look.

The distinction is not reliably the backsplash or lack of it; as weissman points out, there are free-standing ranges without backsplashes and there are also slide-in ranges *with* backsplashes. The only distinction between the two that is always reliable (I think :)) is that free-standing ranges are finished on the sides with a sheet metal "skin". In other words, they can be at the end of a cabinet run or by itself - "free-standing". Slide-ins are not finished on the sides and therefore *must* be installed between cabinets unless you're into a very industrial look.

It's true that *typically* (but not always), as weissman wrote, a slide-in overlaps the adjacent counter - no gap. Most lack the backsplash and so oven controls must be on the front. In free-standing, the electronics usually go in the backsplash and so generally do not need a cooling fan. Without the backsplash, a slide-in's electronics end up wedged between oven and cooktop and very often are cooled by a fan. Some people complain about either the noise or where the hot air comes out on some models. Finally, as weissman also wrote, by shopping for slide-in, you identify yourself as somebody willing to pay extra bucks for a "look" and so manufacturers charge more. You get less bang-for-the-buck in terms of features/specs per dollar.