There are two main types of folding umbrellas: 2-fold and 3-fold umbrellas. The key difference between them is in their skeleton structure - a 2-fold umbrella can fold into two sections while a 3-fold umbrella can fold into three sections, making it more compact. Other differences may include cost, size, style and intended use. When choosing a folding umbrella, factors like the handle material, cloth quality, shaft type, and overall size should be considered depending on individual needs and preferences.