Ball valves use a rotating sphere as the control element, with a hole through it the same diameter as the pipe. They are intended as isolation valves:
A buttefly valve is similar to a throttle in a carburettor. It is used to give a degree of proportional control to a flow
The third kind of valve is a gate valve, which like a ball valve is used for shutting off flow:
Incidentally, a globe valve is not the same as a ball valve, despite what google thinks.
A ball valve uses a ball as the closing element. A Globe valve has a screwdown valve inside a globular enclosure. The are used as stop valves in high pressure systems, like steam globe valve