Since any map projection is a representation of one of those surfaces on a plane, all map projections distort. Every distinct map projection distorts in a distinct way. The study of map projections is the characterization of these distortions.
If you have the car as collateral, the loan company will take the car. The co-signer is not automatically put on the title, that would be between you and the co-signer. My father co-signed a loan when I was younger, and my name was on the title, not his.
Then when you pay off the loan on your car, the lender has your title printed and you get it in the mail usually about a week later, signed or stamped to indicate the lien is satisfied. There are 2 examples below of vehicle titles where the loan was paid off.