A lot of brushed motors have magnets in too; they're just on the rotor (rotating part) rather than on the stator (stationary part). Some brushed motors use a wound field (especially mains ones which put the field in series or parallel with the armature such that they'll run on AC current), but the power density from permanent magnet brushed DC motors is higher so they're probably more common in cordless tools, especially those with reversing switches.
Every brushed cordless tool I have repaired have had a pair of strong permanent magnets glued into the outer casing of the motor, never seen them on the rotor. I think they are called a universal dc brushed motor.
Dewalts mostly use these universal motors, a similar motor is fitted to Ryobi, Bosch & most cordless tools but they all have a different drive gear on the shaft that makes swapping them impossible!

Makitas use a unique motor with the stator & rotor separate, meaning you can replace them separately without needing a whole motor.
