Chaps are a leather garment worn over pants. They only cover the legs, and have no bottom or crotch. They are usually worn by cowboys, to protect them from rope burn or being scratched while riding through thorny bushes. Chaps are usually made from leather, and modern chaps as seen at rodeos can be very bright and colorful.
A coat is a warm top you wear over other clothes. A coat is very similar to a jacket but coats are usually longer. The word coat can also be used to describe an animal's fur.
A corset is a piece of clothing that was once worn by almost all women as underwear to give them a defined waist. Today corsets are worn as outerwear more for reasons of fashion. A lot of garments today that are described as 'corsets' are just imitation with a corset look, but don't actually shape the body.
Corsets are not usually held shut by zips or buttons like other garments. They usually hook together at the front and are laced up at the back, as you can see in the picture.