Permanent Magnet Synchronous Machines (PMSM) has permanent magnets in their rotor. They are compact, powerful and offer excellent dynamic response. Permanent magnets are expensive and with overheating or overcurrent can partially demagnetize.
Synchronous Reluctance Machines (SynRM) have a rotor made of layers of magnetically soft material. These ferromagnetic layers orient along the stator magnetic field and follow it as it rotates.
SynRM have a cost advantage as they do not need expensive rare earth elements. They tolerate overheating or overcurrent well, as there are no magnets to overheat and demagnetize. Certain designs can also offer advantages at higher speeds. They generally have lower starting torque and poorer power to weight ratio than PMSM. SynRM are more nonlinear and harder to control.