I’ve seen both these terms used interchangably and with completely different meanings. I think it’s important to have a distinction no matter what you call them.
To me a coach is someone who has direct responsibility for training and developing someone else, usually a subordinate. It’s part of their job description and compensation. “I do well, if you do well.” “I want you to win and if you win I win.”
A mentor is someone who doesn’t have the resonsibility but wants you to do well. They want you to win, but they may not win if you win. This is a person you can go to for advice or ask questions. A mentor is willing to help but doesn’t have to.
Which is best? In the ideal situation, you should have both. They offer something different and both can really help.
I’d also add in a third player, a “buddy.” This is someone who is going through exactly what you’re going through and provides support and resources as you learn. In the Gallop survey about what employee’s value, having a buddy is top of the list.
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