From what I've seen and read about them, both use pretty much the same idea - an enclosure with an internal drive mounted inside. The difference is that ones that are marketed as external drives aren't designed to be opened to swap drives. It's probably easy to do, but it's not the intention of the design.
- more choice for hard drive
- more flexibility - the same drive can also be used internally
To add to this:
- get a full-height encloure (5.25") and you can even use optical drives in it.
- get a 2.5" -> 3.5" IDE adapter and you can mount laptop hard drives, too.