There are a few varieties of negotiation practised by mediators, resulting from differing  psychology theory, resolution techniques, differing work backgrounds, and underlying fundamental principles. In practice, the keenest differences  are evident firstly in the style of mediation and secondly in how proactive (orchestrator or dealmaker) mediators wish to be.

Style. Mediation can be either interest based or positional. Interest based seeks to widen the possibilities and attempts to help both parties reach a happy solution or understanding (1+1 = >2) . Positional bargaining involves more focused tactical negotiation and attempts to achieve a willingness to compromise on fixed issues (2-1 = 1). With business or finance negotiation there is perhaps an emphasis on tactical negotiation, whereas in family law with abstract or emotional concerns, third parties to consider,  and a continued relationship, interest based bargaining has much attraction.

Proactive. At its least intrusive mediators simply provide a safe space for disputants to solve their issues. The rationale is that people are capable, should be allowed to fix things themselves, feel most invested by being entirely responsible, and are potentially the least influenced by the mediator. Even here there is some interjection by the mediator so to some extent there is participation and the question is of degree. Some negotiators however do if asked venture impartial opinions on the law, especially if non contentious  and provided they are qualified (as attorneys) to render legal opinion. Further, some  offer potential alternative solutions if appropriate.

At the end of the day, it is probably best to employ whatever technique suits the participants at the time, provided the feeling is of a voluntary process.