There is no difference. Moving an axis is usually done with a stepper or servo motor. A spindle can be driven with almost any motor that has enough horsepower and the RPMs required by the spindle it is driving. On a given mill a servo driving the spindle will likely be larger that the servos moving an axis but it really depends on your requirements.
I chose to switch the standard DC motor on my mill spindle to servo motor that had more HP, better speed control, and an encoder which allows me to do ridged tapping.