1/ Arbitrator

An arbitrator is someone who hears evidence and renders a decision in arbitrations but not in any other type of dispute.

E.g.: If you have a mandatory arbitration clause in your contract you may find your case brought before an arbitrator who works for a private arbitration group.

2/ Arbiter

An arbiter is an impartial person or institution given the power to decide in any sort of controversy.

E.g.: The Supreme Court is likely to be the final arbiter in this long, drawn-out and highly divisive dispute (However, the exception is in Scotland, where arbiters conduct arbitration)