Yes, we borrow from the Latin on some pairs of words, such as employer and employee, and grantor and grantee, but most of the time we don’t. We have parent/child, husband/wife, giver/recipient, boss/underling, master/apprentice (or slave). You can come up with your own list, and I invite you to do so in the comments. So what about “mentor”?
It’s not mentor and mentee! (Mentee sounds like a sea creature that used to be mistaken for mermaids.) The correct term is protegé (accent optional in English). You pronounce it “prota-zhay.” This one we borrow from the French, and leave Latin to its dusty spot on the bookshelf.
We borrow from the Greek, too— “Mentor” is an eponym. It’s the name of Odysseus’ teacher. Remember the Odyssey? That guy. Mentor was an old, wise fellow, who was instrumental in saving Odysseus’ marriage. It’s an interesting story.
One last tip: to get that high-class accented “e,” hold down the Alt key while you type 0233 on the numeric keypad. Then lift the Alt key and “é” appears.