The sound, for starters.
Sheet cymbals usually have some harsh overtones in the upper range. They sound pretty trashy. I actually like some of them. And some of them aren't fit for anything.
Physically, their appearance is not that different from cast/forged cymbals. Sheet cymbals are usually thinner, lighter, and aren't hammered or hand lathed. You can usually hold one in each hand and feel the difference in weight and just overall solid-ness. A cast/forged cymbal starts as a chunk of alloy and gets pounded and formed into shape. Then it's finished off by hand, or by machine run by a human. The sheet cymbals come off a roll and get stamped out like cookies. If a sheet cymbal is actually lathed, you can usually still tell it's a sheet metal cymbal because the lathing will be evenly spaced and very precise, like a machine did it. The quality cast/forged cymbals are hand hammered and lathed, and you can tell this by the random pattern of hammering and lathing. Some good cymbals are stamped from sheet metal made from a good alloy, but usually the stamped sheet cymbals use a cheap alloy and even cheaper manufacturing. There might not be human hand on a sheet cymbal until someone puts the price tag on it. But there also very high quality cast/forged cymbals that aren't hardly finished at all. Most of the major cymbal makers have a line that isn't lathed. A Paiste RUDE looks like a piece of shit manhole cover, but it surely isn't. You just gotta listen to them and do some research.
