FM radio is not really a good comaprison. The incoming radio signal is still a sine wave, but with the frquency constantly changing. This is then converted to an an audio frequency analogue signal, without (necessarily) a digital stage - it is never converted to and an on/off signal, whereas the output of a class D amp, or a PWM motor drive is.
(When I say output I mean the output from the switching devices)
Most modern motor drives have DSP controllers anyway. I really don't now if the Class D amps are DSP controlled or analogue.