The difference between a cosigner and a co-borrower is this:
In either case, both cosigners and co-borrowers must go through a credit check to gain approval for a car loan.
Another major difference between the two is how your loan works. If you want to remove a cosigner, you simply have them fill out a cosigner release form. For co-borrowers, the process is far more difficult, and typically, you have to refinance the car to remove the co-borrower.
More: How to get a cosigner for a bad credit car loan