There are multiple types of shorts:
Track shorts: shorts that reach only the upper thigh and are intended to provide maximum freedom of moment in sports activities.
Walking shorts: Shorts with a long pant length reaching to the knees which is intended for casual wear. Usually has pockets and waist loops for a belt and is worn with or without that.
Cut-offs are homemade shorts made by cutting the legs off trousers, typically jeans, above the knee. The cut is not finished and the fabric is left to fray. Originally a practical use of trousers whose knees have worn through, they are now a type of shorts in their own right.
Hotpants: commonly known as "short shorts" are primarily worn by young, hot, women. These are short, tight shorts, usually made out of cotton, nylon, or some other common material. They are meant to emphasize the buttocks and the legs.
"Skorts" are shorts that have a piece of fabric in front so that from the front it resembles a skirt. It is a contraction of "skirt" and "short".