Besides reality game shows, you can also get booted out of nightclub for being too drunk. You can get the boot (get fired) at work. A boot is also a type of punishment where a lock is placed on a car's wheel so the car can't move. Example: The driver got booted for not paying his many parking tickets.

To kick out. I've only heard this when talking about a competition like on the voice or X factor, contestants who aren't good enough get booted off. You can also hear this a lot on other competition type reality tv shows.