The mediator serves as a neutral facilitator. In mediation, the parties must agree, or their is no resolution. Its much more participatory - that's one of the reasons for its success. The parties have more owner-ship over the resolution since they crafted it. Most urban communities have community mediation centers that provide services free of charge or for modest charges.
Some courts also sponsor mediation programs.
And there are privatemediators available. Yes - but there are no uniform requirements, which is why its' important to make surethat a mediator you select has had sufficient training. I received training from the DC Superior Court and now volunteer as a mediator there. An arbitrator serves in a more informal setting than a judge - outside the courtroom. Typically, the rules of evidence do not apply - its a much less structured process.