A moderator is in charge of “moderating” participatory behavior in an organized collection of people, whether an online or offline forum, a gathering or a meeting. A moderator follows specific rules of engagement and moderation and his engagement is reactive to what happens during such a meeting/gathering.
A mediator, mediates between two or more parties to achieve a common-ground or a mid-way for all parties in solving a certain conflict or a problem, following their wishes and desires. His non-biased involvement is invited by all parties and is he has no entangling relationship to the conflict or problem at stake.
A negotiator enters into a negotiation process with one or more other parties to achieve predefined objectives or realize a certain interest of his own or ones that he is protecting on behalf of others. A negotiator aims to reap the most gain possible from a negotiation and incur the least loss/harm possible. A negotiator is, mostly, very involved in the issue/problem at stake, being either one of the conflicting parties or one that is directly or indirectly affected by it or entrusted with finding a solution for it.
A conflict-resolver can be a moderator, a mediator or negotiator with a clear-cut predefined objective of solving a conflict or it can be a UN-diplomat! The big difference with others is that the conflict resolver is endowed with certain authority to actually enforce conflict resolution or draw a road-map for involved parties to follow-through with its directions, independently.