A mentor gives you the step by step approach, he already went through the problems you're facing.

A coach makes you think.
He asks questions.

You can think by yourself, but you don't realize you're being stuck in your own pattern of thinking, and coaching is to give you a different perspective, to give you a nudge so you can be set on a different track.

Sometimes you only need one shift, one question you never really thought by yourself.

Coaching makes you think more deliberately. Most of the time we're lazy to think. To set goals, to ask what we really want, thinking strategies.

As a coach, the easy part is to give advice, or what I would do, or what other people did. Because I read a lot of literature on self-help.
But the trick is: It's not a lack of knowledge that keeps you blocked. It's more your limiting beliefs you're not aware of.