TextileGlossary.com

Shorts are a garment worn by both men and women over their pelvic area and the upper part of the upper legs or more, but not the entire length of the leg.
They are called "shorts" because they are a shortened version of trousers (as they are called in British English) or pants (in American English) which cover the entire leg.

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".

A half pant worn on the waist having length up or above the knees, generally worn by children and also by adults.

.short pants: trousers that end at or above the knee
.drawers: underpants worn by men

Shorts are a garment worn by both men and women over their pelvic area and the upper part of the upper legs or more, but not the entire length of the leg.