English Discipline: Let's start with the tack. Unlike Western, in English the bridle (The equipment on the horses face and the reins which go around the neck) has nose band which can come in several types depending on your style or what your doing. The saddle (The equipment that goes on the horses back which the rider sits on) does not have a horn and is usually either a jumping saddle, dressage saddle, or an all-around saddle. It is also common for there to be two saddle pads, the main one which is larger and sort of like a square, and then the half pad for extra cushion. In English, the technique is fancier and more revolved on equitation (your position) and the way you ride your horse. Also the main different styles of riding in the English discipline are Jumping, Dressage, and Cross-Country. There are also others such as polocrosse, vaulting, gymkhana, etc. Also it is much more common in English to wear a helmet and is looked down on to not where a helmet.
Dressage
Stadium Jumping Cross Country
Western Discipline: (disclaimer: I don't actually ride western and don't know as much about it.) In Western, the bridle (The equipment on the horses face and the reins which go around the neck) does NOT have a nose band. Also the saddle (The equipment that goes on the horses back which the rider sits on) DOES have a horn for the rope to go on and it is a lot heavier and chunkier. The saddle pads are usually thick and blanket-like. In Western they focus more on speed and they have barrel racing, pole bending, Reining, Cutting (cutting a cow off from the herd in a certain time limit), etc. It is also more common to wear a cowboy hat instead of a helmet, no helmet at all, or a helmet disguised as a cowboy hat; although it is becoming more popular to wear helmets.
Cutting
