What is the difference between a jointer and a rabbeting jointer. And can a rabbeting jointer be used to just plane the edge of a board?

You can use a full sized joiner for rabbiting joints, just by using the edge of the joiner blades, a rabbiting joiner sounds like a smaller version of a full sized unit.

If, a specific machine is listed as just a rabbiting joiner, probably, no, you can't do just the edges or small surfaces, only rabbit joinery.

Sorry couldn't be more specific on the rabbit joiner info, perhaps someone else will have a little more on that unit.

KBC

Typically a rabbiting jointer is a standard jointer with the addition of a ledge that allows a 1/2 inch rabbit to be cut. Most of the rabbiting jointers I've seen are 6 inch versions which would allow it to be used to plane the edges of boards like you are wanting to do.