As to outcome, an arbitrator makes the decision and is responsible for the quality of the decision. By contrast, a mediator facilitates parties reaching their own decision and is neutral regarding the outcome. In mediation, parties are responsible for the quality of the decision.
The arbitrator is the enforcer of the process, limits exchange between principals, limits scope of information and communication and assesses facts. A mediator facilitates and encourages exchanges between principals, broadens the scope of information and communication, and helps parties assess facts for themselves.
Finally, an arbitrator is blind with respect to the parties and their backgrounds, has high expertise in rules and high power over the principals. A mediator has high expertise in social process, low power over the principals and may have moderate knowledge of the parties and background.
I cannot imagine arbitrating a case that has not first been mediated. Arbitrators do not replace mediators; they are a substitute for judicial decision-making when mediation has failed.