In my experience a protectorate becomes an ally that will pay you tribute (sometimes a lot of tribute). Protectorate cities do not require garrisons like a conquest would. You can’t enter or raise your own troops in their cities but neither must you manage them. You have total military access to protectorate land in all other respects. I believe that all of the protectorate’s territory counts as your own when the game counts areas controlled.

You don’t control a protectorate’s armies but they will defend themselves saving you some effort at the very least. I have never seen my protectorates invade anyone. The only protectorate that ever reneged on me was the Senate when I made war on the Scipii. Since the Romans are a special case it may be that protectorates are otherwise very reliable.