what is the different betwean AC brushless motor and DC brushless motor?

I believe the difference is that you can drive an AC brushless motor
directly from an AC line - 50 or 60 Hz.  I am not sure this is the same as a
synchonous motor or not. Perhaps you should quote the motors or source of
your information.

A DC brushless motor one needs a controller to 1) sense the position of the
the stator and 2) change the current flow in the coils in order to generate
the next phase of rotation. These are more typical for robotics and more
expensive in relationship to a brush DC motor.

Brad Smallridge
Ai Vision