This was talked about deep in another thread. So I thought I'd make one that was titled properly.
After looking at the brushed/commutator DC motor, I can now see have a two pole brushless DC motor was considered a DC derivative. The brushed DC motor did have a "controller" integrated into the motor. So the name of a motor type does consider the controller, at least along this line of evolution.
A lot of disagrams that try to explain motors in simplified ways can be misleading. Look at:
formatting linkyou ever seen a magnet that is "all North" or "all South"? Of course there is no such thing and the motor is not really built as shown. But I wonder how many people might end up thinking there are such magnets when they see something like this. It might seem plausible to some people to just cut a bar magnet in half.
This site has a lot of cool pictures: