The wound rotor synchronous machine is generally designed to have a sinusoidal distributed rotor magnetic field. Also as the rotor field current may be controlled it can also control the reactive power supplied or drawn once synchronised to the mains.
A PMSM machine may have the rotor designed with both a sinusoidal distributed or square wave distributed flux; the latter commonly known as a BLDC.
As such reactive power control is not possible with PMSM machines although as a motor one can use power electronics to do field weakening etc.
The main difference is that wound rotor machines are normally fixed frequency machines whereas PMSM/BLDC are used for variable speed applications mostly in machine tools and small high performance servo applications. Some large ships now also use them.
1- In PM synchronous motor and during starting operation with speeds less than the synchronous speed, the permanent magnet flux induces in the stator winding an emf of a frequency other than that of the supply. This emf causes current to flow in the stator winding circuit which interacts with the rotor flux and produces a drag torque. This drag torque opposes the driving torque. This is not the case in classical SM where the field winding is short circuited at starting and not connected to dc supply. so the PMSM can be treated as the classical one but with constant field current.
2- In salient pole PM synchronous motor, the direct reactance Xd and quadrature reactance Xq are fairly close, in contrast to conventional SM. The principal cause is the very low permeability of PM itself. This sometimes makes Xd is a little bit less than Xq!!! and hence the reluctance torque may be negative.