Above is a western saddle. As you can see, it has a broader seat than that of the English. It has a horn that you can tie a rope around if you like, and the saddle pad on a western saddle isn't attached like that of the English saddle.
Western style riding can be used for jumping, like English, but is better for trail riding, rodeo, rounding up animals such as cows, and pleasure riding.
You can show with western, just like you can with English. There are halter classes in western, and cow roping contests. There are also many others.
At Claudia's house, I ride western. I ride in a small black saddle on her gray fifteen year old Quarter horse gelding, Shiloh.
Sometimes I ride Rio, her bay gelding. And sometimes I ride Johnny Rebel, her paint gelding.