They are different. This is my understanding:
If you mediate between people, you are a go-between. A mediator helps the two parties to communicate and to settle their differences themselves. The mediator simply facilitates the discussion, but the parties come to their OWN decision.
If you arbitrate between people, you are more like a judge or referee. An arbitrator gets each party to to explain their position and views, and then makes a judgement FOR them.