[FungalRaincloud]

In a brushless DC motor, the rotor is a magnet, and the stator is a series of electromagnets that can be powered independently, yes. But the rotor is still usually at the center. You're dead right on why it can be brushless - the bit that moves is the permanent magnet. One other important difference is that the coils need to be controlled by a computer of some sort to get the timing right to make a rotating magnetic field and keep the magnet spinning.

[tonyarkles]

And just for reference, at least in the hobby community, these are called in-runners and out-runners. An in-runner has the rotor on the inside and just a shaft that sticks out; an out-runner has the stator on the inside and the outer body of the motor rotates.