Divorce attorneys will negotiate your divorce terms for you, and go to court with you if negotiation fails. The attorneys will do the talking, and you and your spouse are usually encouraged not to speak to each other. The judge makes the final decisions.
Divorce mediators encourage you to to speak for yourself and your needs, and work with both you and your spouse (often together and alone). It usually costs significantly less than any of the other options. Trained divorce mediators are mostly either attorneys or mental health professionals (or sometimes others who have been specifically trained to do this work). Mediators often encourage clients to hire a mediation-friendly attorney just to make sure you will not sign an agreement that is not in your best interest.
Collaborative Divorce is where each spouse hires an attorney trained in collaborative law, as well as a coach who is a trained therapist. The parties agree to negotiate in good faith, and work towards an agreement that is collaboratively created. The meetings are five-way, and include clients, attorneys, and the coach.