"I think the misunderstanding may be that a switch mode power converter (eg an MPPT controller or any type of DC-DC converter) internally uses switching transistors, it is therefore a PWM controller."
Nobody said that. What was said is that the MPPT controller uses PWM in Absorb and Float without MPPT, same as a PWM controller does. Nobody said they are both "PWM controllers"
It is understood that a "PWM controller" does not have a buck converter in it and an "MPPT controller" does. The buck converter is working even when the MPPT controller is doing 12-12. The PWM controller can do 12-12 or 24-24, but not 24-12.