BTW, someone said that Class D is not "digital" which is partly true, but PWM is a digital signal processing technique, so it's understandable for those amps to be called "digital" especially from a marketing angle.Just had to put that in there.... that 'someone' being me...
Class D was first demonstrated during the vacuum tube era. The reason it is called 'class D' is that class C came before it and so was already taken. PWM (Pulse Width Modulation) is an analog technique. Just ask any keyboard player with an analog synthesizer (by varying the pulse width, a string sound can be obtained from a square wave).
From the Wikipedia page (https://en.wikipedia.org/wiki/Class-D_amplifier):
The term "class D" is sometimes misunderstood as meaning a "digital" amplifier. While some class-D amps may indeed be controlled by digital circuits or include digital signal processing devices, the power stage deals with voltage and current as a function of non-quantized time. The smallest amount of noise, timing uncertainty, voltage ripple or any other non-ideality immediately results in an irreversible change of the output signal. The same errors in a digital system will only lead to incorrect results when they become so large that a signal representing a digit is distorted beyond recognition. Up to that point, non-idealities have no impact on the transmitted signal. Generally, digital signals are quantized in both amplitude and wavelength, while analog signals are quantized in one (e.g. PWM) or (usually) neither quantity.