If you take out a private-party auto loan (a loan to buy from a private seller), the money goes to the seller through any number of avenues. Most commonly, the bank will provide you with a cashier’s check made out to the seller. When you go to purchase the car, hand over the check and you’re done.
In other cases, and more specifically if the loan is from the same lender where the seller does their banking, the lender can simply transfer the funds into the seller’s account. Rare instances may also allow for a wire transfer, though these are becoming less and less popular due to the chance of fraud.