The style of English riding is seen more of an elegant style compared to the relaxed western. The English riding started over in England and was mostly used for sport like fox hunting and polo.
When riding English it is done at a faster rate the western. Also when trotting you post, which is rising up and down in the saddle with the beat of your horse. The English saddle is also quite different then the western saddle, it is much smaller and doesn't have a horn.
English has many branches of disciplines much like western. There is stadium jumping, cross country, and dressage, which all make up eventing. Eventing is where those three events take place over a three day period and all your scores are combined to see who wins. These disciplines can also be performed separately.
Endurance is also another form of English riding and is where horse and rider travel long distances at a steady pace and compare times with the other riders to find a winner.
Hunt Seat or English Pleasure is the "western" of the English disciplines. The main goal for English Pleasure is to show how much of a pleasure your horse is to ride.English Equitation is just like Western Horsemanship it focuses on the rider's capability to control and ride their horse. You are scored on your riding skills as well. Most of the time you perform a pattern with your horse.
Here are some sites that will have more information on English disciplines:
