And, since nobody has mentioned it yet, I'll add that there are NO FLUIDS in either type of motor.
Topologically/ semanticly debatable whether it is technically inside the motor, but the S/X (possibly 3 front) induction motors have a coaxial coolant loop in the rotor. That is the same coolant loop as the rest of the car, so nothing extra to change.
Normally when people say “permanent magnet motor” they mean a standard permanent magnet synchronous motor like in the Bolt. The model 3 rear motor apparently uses a new kind (for EVs) called a switched reluctance motor. From what I’ve read this requires a much smaller amount of rare earth magnetic material, and is cheaper and more efficient than the AC induction motors used on the S and X (and the smaller Model 3 front motor for AWD variants).
The 3 rear motor is a permanent magnet switched reluctance motor (PMSR). It is distinct from a pure switched reluctance (SR with no magnets) or a permanent magnet (PM) motor. A PM motor can be mechanically commutated (brushed) or electrically (brushless).
Basically, in an SR motor, the starter (outer) winding generates a magnetic field and the rotor (center) aligns to the field (changes reluctance). Similar to switching on a series of electromagnets to move a piece of iron.
Tesla adds in some permanent magnets to (likely) shape the fields to reduce torque ripple (force is stronger when the iron is almost aligned). The magnets also provide a stronger force at low stator field levels. (Like a magnet to a magnet vs magnet to iron).