Permanent magnet brushless AC motor (PMBLAC) and permanent magnet brushless DC motor (PMBLDC) are same physically. For PMBLAC, the supply is a sinewave, whilst for PMBLDC, the supply is trapezoidal wave. However, with the trapezoidal wave supply, the output torque tends to have more ripples.
For a 3-phase induction motor, with a 3-phase sinewave ac supply, the torque you get will be smooth or constant. In my opinion, it's not necessarily a sinewave voltage to drive an induction motor. The main idea is to supply a voltage to the induction motor so that it can produce a rotating magnetic field. If the rotating magnetic is constant, then you will get constant torque. If the rotating magnetic is not constant (like in single-phase induction motor), then the torque is not constant. At high speed, the vibration caused by torque ripple is filtered out by the mechanical load.