I am located in Texas, but I want to buy a car for my granddaughter in Albuquerque, NM. Is there a tax difference if I buy it in either state?

No. You pay the Texas rate.

You will not pay any sales tax when you buy the vehicle in New Mexico. When you title and register the vehicle in Texas you will pay the sales tax then. If any sales tax is due to New Mexico, Texas will send it to them. I live in New Jersey and bought a car in North Carolina. That's exactly what I did. I didn't pay sales tax to North Carolina, I paid New Jersey when I got the car home. Hope that helps! Jim