Are stator and rotor pole numbers always equal in a synchronous motor?

I want to know when it is mentioned number of poles of a synchronous motor, i assume the poles will be same on both stator and rotor. For example: 4 pole synchronous motor, 4 poles on the stator and 4 poles on the rotor. Is my understanding correct? Please advise.

I've always thought that the number of poles of a synchronous motor referred to the number of field poles.  If the field rotates (like in many permanent magnet motors) then the "poles" are on the rotor (in pairs, of course).  But the field can be in the stator too (requiring slip rings to the rotor so not very common).  And I have seen plenty of permanent magnet synchronous motors with rotating magnets and  many more teeth in the stator that poles on the rotor.  So, in this case, if what you mean by poles on the stator is the number of teeth the windings are wound on (often referred to as the slot count, the slots between the teeth that is) then, no, they do not have to be the same.  My understanding is the designers adjust the slot count to affect magnetic cogging and maybe torque ripple? Is there a motor designer here that can help clear this up?Best - JD

Excellent, thank you very much for the information of great importance and excellent quality for all of us and that example that you did not say is very, very good to understand your point