How would you describe a mentor vs coach? Do they mean the same to you?

To me, a coach is somebody who helps develop you in a specific functional area, for example, in your sport, in your career, or in a trade. A mentor is somebody who helps develop you more broadly as a person.

To me a mentor is someone that I tried to be like and guided me. A coach was someone that taught me how to do things. To me they are/were different but they could be the same.

Coach as a noun, is a paid position. Mentor as a noun is a position of respect. As verbs, both are very similar.