This is going to sound like a dumb question, but since I have no idea, I'll ask anyway. If I buy a ball head, can it be used on both a monopod and a tripod, or would they be different types/serve different purposes?
Can you use a tripod head on a monopod? Yes.
Do I personally see the point? No.
I find a simple pivot head to switch from landscape to portrait orientation to be all I need on top of a monopod. Any other direction of movement I tend to accomplish by leaning the monopod. IF I want to tilt to an extreme angle I align the pivot with the intended angle of movement and add it so that I don't move my camera's center of gravity too far away from the base of the monopod.
This behavior is based on my opinion that the entire point of a monopod is to be light, simple, and always with you. Adding a tripod head of any decent size can quickly double the weight of your monopod.
It's for this reason, also, that (in response to the OP) I bought a CF monopod long before I splurged and upgraded my tripod.