Motors that work directly on AC do not have commutators. Commutation refers to converting DC into AC inside the motor, and is done, in a DC motor via commutators.
In a typical brushed DC motor, at the very least there is one winding on the rotor (collectivelty called "armature") that are connected to the commutators at one end. A pair of brushes contacts the commutators. When DC is applied, a magnetic field build up and the armature spins in a direction as per the polarity. As soon as the armature has moved by 180 degrees, the commutation causes the applied voltage also to reverse - this again causes the armature to keep rotating in the same direction. So the winding moves 180 degrees and then has a polarity "correction" which is the same as applying +ve and -ve pulses alternatively - an AC voltage.
In a brushless DC motor, the commutation is done electronically via transistor or FET switches - arranged in a half or full bridge configuration which simply alternatively applies pulses to the coil. In these motors the winding remains stationary but the magnet is caused to spin.
