What's the difference between Advisor and Mentor?

In the context of your question the answer of Bryan Krause is almost certainly correct - no real difference.

But in a wider context, the idea of a mentor is a bit broader than that of an advisor. An advisor will usually have some official relationship as an intermediary between a student and the university with official responsibilities. A mentor, on the other hand, can be quite informal.

In my doctoral studies I was lucky to have both. My advisor advised me on the specific doctoral work and the field. But I had a separate mentor in a quite different mathematical field in which I was much less adept. But he was and remains my role model for what a faculty member should be and he gave me good advice and aided by development at one critical point.

With that in mind, you normally have one advisor (exceptions exist), but you can have several mentors.

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.

The answer depends very heavily on local custom. In my university as a PhD student I have a Supervisor and also an Advisor who are not the same person. My supervisor is there to guide my research. My advisor is there to guide me in anything that I do not want my Supervisor to guide me in, for example, if I thought that my Supervisor was doing a bad job. At some quite important meetings, such as annual reviews of progress, my Supervisor plays no role and is not present, but my Advisor is.

I have been a Mentor, but neither my Supervisor nor my Advisor perform that role for me in my university.

I do not claim that this system is right, but I describe it to show that there is no universal language that describes the different roles that might be invented in different universities to perform the same basic task.

So, the OP's question cannot be answered without knowing which institutions in which countries are being referred to.