Horse shows are held throughout the world with a tremendous variety of possible events, equipment, attire and judging standards used. However, most forms of horse show competition can be broken into the following broad categories:

Equitation, sometimes called seat and hands or horsemanship, refers to events where the rider is judged on form, style and ability.

Pleasure, flat or under saddle classes feature horses who are ridden on the flat (not jumped) and judged on manners, performance, movement, style and quality.

Halter, in-hand breeding or conformation classes, where the horse is led by a handler on the ground and judged on conformation and suitability as a breeding animal.

Harness classes, where the horse is driven rather than ridden, but still judged on manners, performance and quality.

Jumping or Over Fences refers broadly to both show jumping and show hunter, where horses and riders must jump obstacles.

Original article: https://en.wikipedia.org/wiki/Equestrianism#Horse_shows