Horse Discipline
Training discipline is the most general method of training a horse. It comes down to either more or less management when cueing a horse to do something. This is different from riding discipline.
Pick Your Path
English
English gives the rider more control over the actions of the horse in a way that doesn't conflict with the horsemanship type you selected. English trained horses learn to follow an exact pattern over time, limiting the reason for a horse to try new ways to complete a set of instruction given by the rider.
Western
Western involves giving the horse more freedom to choose how he complete's a set of instruction. Many western riders think of riding a horse as watching a movie as the horse does all of the things basically for them without need for direct control over each action the horse takes.