"auto" is used and will be understood.I always thought it is just personal preference to use one or the other, but it seems to be regional - in some regions it is used as a common synonym to "samochód", in other it may be considered old-fashioned or childish. I personally would use "auto" when talking about my car as an object, but not about a car as a means of transportation.

But yes "samochód" is a preferred word for a car.