What are the differences between Trainer and Facilitator?

Facilitator: Someone who has the skills to moderate and run sessions, exercises, discussions and work groups where knowledge is shared by and extracted from the participants themselves.

Trainer: Someone who has knowledge and practical experience in a specific topic that he/she transfers via sessions, exercises, case studies, examples along with presentations and what not. So if you want you can consider a trainer to be a blend between a Teacher/Instructor and a Facilitator. Thus the personal skills are as crucial as the knowledge and expertise of that person.