DC Motor EMF re-usage?
The second type is a brushless DC motor with Hall Effect internal commutation or a stepper motor with stronger magnetic attraction for pulse rotation with a full bridge from phase to phase. 

The resting position is determined by the closest magnetic pole position and will be random. Shorting out the coil after power off will stop it more abruptly.  Sensing rotor position can be used to control it's stop position if you wanted, but shunting the motor would effectively shunt the BEMF voltage to maximize current to brake the motor.