Author Kristi Hedges, in her book, The Power of Presence, provides these explanations of the roles of a coach and of a mentor and how they differ from each other:
The Coach shows empathy through a mixture of tough love and strong support. The coach is not afraid to push you because she sees the best in you. This leader has a good sense of what's going on in the rest of your life and isn't afraid to mention it as it relates to your performance and potential.
The Mentor makes you feel that your success is always top of mind. Mentors have your back to guide you along in your career. They will act as a confidante as you hash through ideas and won't hold it against you as your iterate. Because they have done well, they operate from a point of helping others do the same.