A role model can be anybody someone admires and wants to be like. You don't have to know the role model, and the role model doesn't need to know you. A kid can admire someone like a professional athlete, actor, or even a character in a book or movie and decide he wants to be like him/her.
A mentor takes an active role in guiding someone, either with life goals or with specific career/job/educational aims.
A mentor may or may not be a role model, and a role model doesn't have to be a mentor at all.