There are basically two disciplines, Field and Target. It's slightly more complex than that, but it'll do for now.
Target Archery is the one you see on TV. It's usually indoors, marked distances, concentric circle targets, sights, stabilisers, cricket whites, expense.
Field Archery is almost exclusively outdoors, usually in a designated woodland area (a la paintball or clay shooting). Intuitive shooting, targets are pictures of animals, bows ranging from longbow to Rambo, wellies and bodywarmers.
If you want to get started, I'd suggest going to a couple of local clubs to get the feel of things before spending any money. Field and Target have a very different vibe, so what works for me might not work for you.
Personally, I find Target archery to be clinical and boring, and Field to be a lot more fun. Target archers might argue that they don't want to get their arrows dirty, or something. Who knows, they're a funny bunch.