Most of the shrimp in peoples tanks are considered ornamental shrimp. Only certain ones will actually clean fish.....scarlet (or skunk cleaners) are the most popular. There is the fire shrimp that will clean fish, but not as often. These are very pretty, but tend to hide a lot, (also more expensive). Peppermints are popular, but do not clean generally, they are scavengers. All the other types of shrimp are ornamental.
You can house different types of shrimp together as long as the aquarium is large enough for them to pick out their territory. (And no aggresive fish that will make dinner of them.)