Misconceptions about PID Controllers
The input to the PID controller is not a position. The input to the position sensor is a position.

The input to the PID controller is a signal that represents a position.

It could be a voltage, or a current, or a digital number. The exact form of the signal doesn't matter, because all it has to do is represent to the controller what the position is.

If it's an analogue signal, the set point will typically be set by a potentiometer or DAC, to put a reference analogue signal representing the desired position into an analogue subtractor.

If it's a digital signal, the set point will be a number representing the desired position into a digital subtractor.

The controller will have means to integrate and differentiate the signal, weight the direct (P for proportional), integrated (I) and differentiated (D) signals (hence PID), add them together, and output them.

If it's an analogue signal, it might drive the motor directly, or via an amplifier. A digital signal could be converted via a DAC to drive a conventional motor, or may stay digital all the way into an ESC to drive a stepper or brushless motor.