Look at brushless DC motors like used on some computer fans - the switching of north/south poles on the stator is handled by transistors that switch back and forth instead of brushes and the armature is permanent magnets.
If you take a universal motor like used in a corded power drill, it does run on AC current from the wall but will also run on DC because its really just a DC motor with the stator and armature wound in series. Sure it has brushes that wear out, but its still cheap to build and has great startup torque and speed control that a shaded-pole AC induction motor couldn't touch and is why its used.
So sometimes the distinctions between what is considered an AC or a DC motor can be blurred somewhat by their operation and not just the power source.