Coaches support you on every level of your progress. They are there to act as a mirror and an observer to see your blind spots and help you work through them. Coaches are great when you are striving to reach a goal and level up.
Experts know their stuff. They are formally educated in one or several topics and you can feel comfortable taking advice and information from them. Experts are great at passing on detailed knowledge and skill.
Mentors can provide guidance, support and motivation in your endeavors. They will use their own experiences to suggest your next step. Mentors are great for exploring career paths, setting goals and finding resources.