A coach tutors or instructs a person to achieve a specific goal or skill. In golf, a coach only focuses on the mechanics of hitting the ball. No matter what the area of focus is, a coach specializes on improving one or two areas of development at a time.
Mentoring has a different purpose and goal. Mentoring is the act of guiding, counseling, and supporting. The mentor and protégé endeavour on a broad development goal like becoming a leader. Mentoring encompasses many complex areas of development.