There are several flavours of servo motor, brushed DC, Brushless DC and AC, the latter two are in my understanding one and the same as it is the driving method that determines whether they are classed as brushless or AC.
From the sounds of it you just require a DC motor and not a servo, a brushed DC servo is basically just a DC motor with some other stuff attached (encoder, tacho etc) but they work exactly as you describe so if not requiring position control you can ignore the encoders etc and just apply the voltage and polarity required.
Hood