Paying car payments on a car loan does build your credit score.
If you take out a car loan and make the car payments on time then as you pay those car payments those on time monthly car payments will be reported to the credit agencies as a good payment history.
Then your credit score will slowly rise more and more as long as you pay the car payments on time.
However if you default on the car loan payments and miss a payment or two then your credit score will go down because a car loan lender will report missed payments.
So make sure you make your payments on time and if you are having trouble making a car payment it's best to call the lender and let them know instead of just not paying your car payment.
Also if you fail to make a few car payments then a repossession company will be sent out to repossess your car even without you being there.
A repossession is also not good for your credit score and can affect your ability to get a new car loan again in the future.