Are there different types of bluegill?

Well a bluegill is in the sunfish family and there are lots of different kinds of sunfish.

Largemouth, spotted and smallmouth bass are all sunfish. So are crappies.

As for sunfish that resemble bluegills, check out this wikipedia article on Lepomis (bluegill genus.)

Some people use "Bluegill", like "bream" to denote any (or most) of the similarly shaped or colored sunfish. So, when used in this context, there are different kinds of bluegill. But more accurately (as has already been explained), bluegill are one kind of sunfish.

And don't forget there are even some hybrids in there too.