Gyoza wrappers (aka potsticker skins) are generally thicker than won ton skins, and are especially well-suited to frying. Won ton skins are more delicate and are typically best cooked in liquid, such as in a soup or steamed. Bear in mind that the thickness of either wrapper varies by brand.
See these two recipes pictured below for examples of how gyoza wrappers and won ton wrappers can used in slightly different ways.
Recipe: Gyoza with Soy-Citrus Sauce
Recipe: Pork Dumpling Soup