Are BLDC motors permanent magnet motors also?
People are inconsistent and lazy, which is why we've ended up with this confusing set of names for motors. What tends to happen is that popular motor types get named with just enough words to distinguish them from the previous popular motor type, and the name sticks.
(1) A 'BDLC' motor has a permanent magnet rotor, inside or outside a wound multi-phase stator. It may or may not have rotor position sensors. It is controlled by an electronic commutator, which in model engineering circles is often called an ESC (Electronic Speed Controller). It was named brushless, to distinguish it from its predecessor (2).
(2) A 'Brushed PM' motor has a permanent magnet stator, and a wound rotor supplied through a brushed commutator. The word 'brushed' gets dropped and this is known as a PM motor. Brushed did not distinguish it from its predecessor (3), whereas PM does.
(3) Before strong permanent magnets were available, DC motors had wound stators, and a brushed commutator.
There are other types of motors. For instance a 'universal' motor is essentially identical to (3), with the field and rotor connected in series. They are 'universal' as they will run on either AC or DC.
The three phase synchronous motor is essentially identical to (1), but it was intended to be run from 3-phase mains. Starting needs some auxiliary method of spinning it up to synchronous speed before connecting it.