It is important to realize that a "brushless DC" motor is an AC motor -- that is, it requires alternating-current input to maintain motion in one direction. ("Brushless DC" is a marketing term, not a technical term, originated to emphasize that you could replace a brush DC motor and drive with this type of motor and drive.)
A "brushless DC" motor is best regarded as a synchronous AC motor with a permanent-magnet rotor field, whereas an induction motor is an asynchronous AC motor with a rotor field created electromagnetically.
Ironically, what distinguishes a motor marketed as a "brushless DC" motor or "brushless servo" motor from one marketed as an "AC synchronous" motor is that the AC synchronous motor has a secondary asynchronous torque generation mechanism that permits it to accelerate up to synchronous speed running directly off the line. Brushless DC motors are intended to run off some sort of inverter, and usually with feedback, so they do not add this asynchronous torque-generation mechanism.
But if you had a brushless DC motor already running at 1800 rpm (4-pole), it could run fine off a 60 Hz line. Being a synchronous motor, it would run exactly at 1800 rpm, whereas an ayschronous induction motor would "slip" and run at somewhat less speed, typically 1740 rpm at rated load.
It is entirely possible to use the same stator with an induction motor rotor and a brushless DC rotor. I've seen teaching systems that literally allow you to mix and match rotor and stator types this way.
Curt Wilson
Delta Tau Data Systems