There are 3 main styles of mediation: Facilitative, Evaluative and Transformative.  When speaking to solicitors, I have found that most will be unfamiliar with the terms and, accordingly, I felt a brief summary of the differences might be helpful.  
Facilitative Mediation

In facilitative mediation the mediator structures a process to help the parties to reach a mutually agreeable resolution.  The facilitative mediator searches for parties' issues and needs beneath the parties' positions, asks questions, validates and normalises the parties' points of view.  The mediator helps the parties find and analyse options for settlement but does not make a recommendation or give advice.  The facilitative mediator is in charge of the process and the parties are in charge of the outcome.

A facilitative mediator helps 'facilitate' an agreement but does not impose, recommend or advise.  The mediator will typically hold a joint opening session, followed by private meetings.  The facilitative mediator will try to engage with the parties rather than solely through the parties' solicitors or barristers.

Facilitative mediation developed in the 1960's and 1970's in America, with volunteer mediators and disputes in which there were typically no lawyers present.  Accordingly, in that era, such mediators did not need to have technical knowledge of the disputes subject matter or even the law in that area.  Today, most professional mediators in the UK practise facilitative mediation, and in the UK, it is the type of mediation typically taught.  

Evaluative Mediation

In contrast, evaluative mediation assists the parties in reaching a settlement by pointing out the weaknesses of their cases and predicting what a Judge is likely to do.  Where as facilitative mediators are concerned with the parties' needs and interests, evaluative mediators are concerned with the legal rights of the parties.  There will usually be a cost/benefit analysis of proceeding to Court rather than settling.  An evaluative mediator not only structures the process but also directly influences the outcome.

Whereas facilitative mediation developed in volunteer dispute resolution centres, evaluative mediation emerged in Court-referred schemes in America.  The lawyers worked with the Court to choose the mediator.  The lawyers maintain an active role in the mediation, and there may be meetings between the evaluative mediator and the lawyers without the parties present.  Evaluative mediators will frequently have technical knowledge or even expertise or legal knowledge of the subject area in dispute, and this is likely to have influenced the selection of that evaluative mediator.  Most evaluative mediators will be lawyers.

Transformative Mediation

Transformative mediation is the newest of the 3 concepts.  It was named by Folger and Bush in their 1994 book 'The Promise of Mediation'.  Transformative mediation is based on the values of 'empowerment' of each of the parties and 'recognition' by each party of the other party's needs, interest, values and points of view.  Any or all of the parties or their relationships may be transformed during the mediation.  Transformative mediators meet with parties together, since only they can give each other 'recognition'.  Transformative mediators allow and support the parties to determine the direction of their own process.

In transformative mediation, the parties structure both the process and the outcome of the mediation and the transformative mediator follows their lead.

Conclusion

There is sufficient room in mediation for many styles.  Each has its usefulness and there may well be times when many mediators use a combination of these styles.  Some parties, solicitors or barristers may seek a mediator with a particular style for a particular dispute.  Indeed, some solicitors have said to me that they may, on occasions, seek a mediator with a particular style because of a particular party to a dispute.  Assisting parties and lawyers in becoming clearer on what mediators offer can only enhance the usefulness of mediation.