The job of a teacher is to work out exactly what a student already knows, what they don't know, and how best they will learn what they need to.
Meanwhile, a coach knows to implant key study skills on the student, and offers careful criticism and advice to help them improve their ability to learn and to grow as a person.
Finally, an effective mentor will reduce the element of stress in a lesson as much as possible, as the human brain learns better in a relaxed state. A mentor teaches at the point just outside of the student's knowledge comfort zone without going so far as to induce panic: if you create a situation where failure is positive, they will be more willing to take risks and thus more likely to learn.
Here is Mark's highly technical illustration!