[kennyt]

Class A use full power all the time, so they are always ready to output it. They run hot and eat up electricity.

Class B switches on and off as needed, saves power and heat

Class A/B works like class A to a point, then uses class B type switching for the higher outputs.

D are digital or switching amps, they've been around a while but people are really just getting them accepted by the high end. No, all solid state amps are not digital amps.

This is obviously only a brief overview, but will give you the idea.