In the traditional sense, a mentor is someone who you turn to for advice.
Professionally, a mentor can be someone who's worked in the field you're in, or who's had similar jobs as you, whom you seek guidance from. Young professionals are often told to seek mentors. The reason for this is to have someone to bounce career questions off of as well as someone to help shed light on certain workplace situations that commonly come up.
While the common image is that of a young professional and an old mentor, peers or younger individuals can also serve in this capacity; it's the relationship dynamic that determines the mentor/mentee interaction, not age or demographics.
In the career development realm, a sponsor refers to a workplace advocate. A sponsor may be your boss or another leader, or even a peer, that champions your work and development.
This could mean an executive who puts your name up for promotion, or who pushes for you to take the lead in a big project, or even throws public speaking opportunities your way. A sponsor actively helps open doors for you.
A sponsorship relationship is more involved than a mentorship in that a sponsor generally puts their professional clout behind their sponsee. In recommending a sponsee for a raise, promotion, or opportunity, a sponsor indicates professional trust in the person they're elevating.
While mentors have their benefits, sponsors have more impact. A sponsor will help you advance while a mentor will give you ideas on how you might advance. Think of it this way: a mentor is like a guidance counselor, while a sponsor is like the college admissions officer. The latter opens doors for you while the former describes possible doors to you.
The tricky part is finding a sponsorship relationship. As you can imagine, it's not exactly a topic of conversation, and it'd be out-of-place to directly ask a boss or senior leader to play this role for you. It's a dynamic you have to nurture organically. Luckily, with the advent of employee resource groups, especially women's ERGs, this type of relationship has much more awareness around it which means it's more likely for senior leaders to actively initiate this type of relationship.