President Trump has expressed a wish to act as a 'mediator, arbitrator or facilitator' in negotiations to resolve the Israel-Palestine conflict. Leaving aside for one moment whether this is a good idea, what does it mean to act as a mediator, arbitrator or facilitator? Despite their usage by President Trump as synonymous, these terms relate to separate and distinct processes.
Facilitation - requires a facilitator to 'make easy'. This could be a discussion or a negotiation but the role is limited to facilitating communication in accordance with the rules which have been agreed by the participants. The result of a good facilitation could be a memo, a good talk or decisions on an issue.
Mediation - requires a mediator to provide a structured process to facilitate negotiation. Although there are different forms of mediation (narrative / therapeutic / settlement / etc.) the difference between facilitation and mediation is that in mediation there will be an issue, dispute or problem that needs to be resolved. As a voluntary process committed to party self-determination, a mediator will work with the parties to provide them with a structure and process to enable them to find solutions within themselves. The result of a mediation will be a mediated settlement agreement and more importantly resolution in respect of the outcome. Mediators aim to achieve 'durable solutions', solutions that will endure and which parties can abide by. No party will achieve 100% of what they want, but enough of their priority needs will be met and the process will be conducted with attention and respect to their concerns.
Arbitration - requires an arbitrator to make decisions on fact and law and to render an arbitral award. The arbitrator is not there to facilitate negotiations between the parties but to act as a decision maker. This process is not about party self-determination but about finding certainty and finality. An arbitration will result in an arbitral award which is a binding decision. Arbitral awards are viewed as very enforceable as they are generally supported by Courts and the NY Convention 1958.
What process President Trump intends to use I am unable to say. However, some time understanding the differences would be a good first step.