They aren't really different, if used in a singular context.
In my experience, "advisor" is synonymous with "supervisor" or "PI": it's the one senior person, usually a professor, who oversees the researcher. For an undergraduate, it's possible they might consider their advisor to be a PhD student or post-doc.
They could also call that person a mentor, and mentorship is a key part of the advisor-student relationship, but others can also be mentors. However, if someone just says "my mentor" to refer to a single individual they probably mean the one person who is also their advisor, PI, etc.
Mentors are important beyond earlier career stages, too. Professors themselves should have mentors, and may even be explicitly assigned mentors at an early career stage.