In the case of a mortgage, for example, co-borrowers are almost always also co-owners. Unlike a cosigner, a co-borrower promises to pay the debt each and every month, not just in the case that you don't. They've agreed to help you pay the debt all the way to the end. And, much like with a cosigner, if you don't pay your half, the co-borrower is on the hook for all of it.
The main difference between a cosigner and a co-borrower is that the co-borrower has the right to use the property secured by the loan, whereas a cosigner does not. When it's a student loan or something similar, this obviously doesn't apply since they can't use your degree as they see fit, although they may still benefit from it.