Dumplings have a thick doughy wrapper made of just flour and water, while wontons have a much thinner wrapper made with flour, water and egg.
The thickness of a dumpling skin can vary but is usually always thicker than wonton skin.
Dumpling skins are generally thicker than wonton skins, and are especially well-suited to frying. Wonton skins are more delicate and are typically best cooked in liquid, such as in a soup or steamed.