Maybe this is a useful way to think about it: I'd argue that doing code review for everyone on a team doesn't mean I'm a mentor to everyone on the team. I'm doing a task that is part of my job -- to coach the team on coding -- and they have to consider my comments whether they want to or not.
But if an engineer approaches me and says "in my last performance review, I was told my code isn't very well structured; can you help me?" and I walk through their code with them, then I'm mentoring. It's skill mentoring, in this case, which, as I said, has the most overlap with coaching. Same activity, but different context.
But as someone else said, this distinction isn't really the important part of what I wrote. So if people disagree on the terminology, that's just fine.
But if an engineer approaches me and says "in my last performance review, I was told my code isn't very well structured; can you help me?" and I walk through their code with them, then I'm mentoring. It's skill mentoring, in this case, which, as I said, has the most overlap with coaching. Same activity, but different context.
But as someone else said, this distinction isn't really the important part of what I wrote. So if people disagree on the terminology, that's just fine.