Let me try to rephrase it in a way:
I think the main difference for me is that I go to the coach to support me to solve problems/matters by myself and they are there supporting my process but I expect them to have less influence on the actual content/solution itself. To summarize the coach does not give advices nor they should impose best practices.
While I go to the mentor expecting them to offer me advice and guidance/best practices.
In this I choose (very rarely) a coach to explore problems that I think don't have a universal solution or the solution is subjective like “Should I move to management or continue on the technical path” or “What is best for me: freelancer or employee?”
And I go to mentor to get concrete advice/guidance on specific matters like “How to increase my income as freelancer” or “How to start a new career in X”.
As I write this it seems that for me I see coach as a person that can help me discover the why and the mentor is someone that can help me discover the how.