Yep, Permanent Magnet AC (PMAC) motors are common types of synchronous motors. They are generally more compact than induction motors for the same power output. Induction motors are generally less expensive.
DC Brushless and PMAC are interchangeable. Oh, and nowadays, you don't need sensors (hall, encoder etc). 'Sensorless' motor control is possible by sensing the back emf of the motor or reconstructing the motor current via (super inexpensive) shunt resistors on the legs of the inverter.
An official (not forum post) article comparing the two: http://www.teslamotors.com/blog/induction-versus-dc-brushles...
DC Brushless and PMAC are interchangeable. Oh, and nowadays, you don't need sensors (hall, encoder etc). 'Sensorless' motor control is possible by sensing the back emf of the motor or reconstructing the motor current via (super inexpensive) shunt resistors on the legs of the inverter.