There are many different types of theater so I'm going to break down the differences between the biggest types.
1. Regional Theater- Regional shows are done at smaller theaters that have their own planned seasons (often just in the summer) where they perform well known shows, and sometimes lesser known shows. Some shows will play regionally before coming to Broadway in order to test the production.
2. Broadway Theater- I've talked about Broadway a lot, but what actually defines Broadway isn't just New York in general. There are 40 theaters that qualify as Broadway theaters, and productions at these shows can be eligible for Tony Awards.
3. West End Theater- The West End is kind of like the Broadway of London. It's a common name for the shows that are professionally staged in London. Like Broadway, it's defined by a certain number of streets.
4. Touring Shows- Many productions go on the road and that's what a tour is. Usually staying in a town for a few days or even a few weeks in some cases they are often productions that have just left/are currently running on Broadway or productions that are aiming to end up on Broadway,