My understanding is that coaching is about helping the individual solve the problem himself/herself.

Mentoring is about adding information or skills such that the individual becomes more capable and thus are able to solve a problem.

Depends where you go, these two terms get used interchangeably (incorrectly IMO) and so there is some semantic drift.

If you were to read Julie Starr's "The Coaching Manual", or "The Coaching Habit", the definition is more or less what I outlined.

If you are familiar with the Leadership Continuum/Situational Leadership, the distinction from there becomes: tell/sell (mentoring), join/consult (coaching).