Class D or Class T
According to Wikipedia, "A Class T amplifier is an audio amplifier IC design. Rather than being a separate "class" of amplifier, Class T is a registered trademark for Tripath's amplifier technologies. The control signals in Class T amplifiers may be computed using digital signal processing or fully analog techniques." The page then goes into detail but I'll not quote all that here. So, it seems that most switching amps are class D, some are erroneously called class T and some really are class T.
But what about the working principle behind it?
There are good reasons why you could call class D amplifiers analog and not digital.
A device delivering power to a speaker is by definition analog. The analog input signal is modulated but is not digital. There are no A-D and D-A converters. Analog in, analog out, analog. Isn't it?
Class D amps are also called switching amps because they're either completely on or off. There's no inbetween. The output is switched at a very high frequency, modulated to the music. A class D amp delivers either all of the current available from its power supply, or none. The voltage doesn't change, but the period for which it is on, does. The longer a pulse is on, the louder the music. This is called Pulse Width Modulation, which is also used in digital. Which explaines why you could mistakely call Class D amplifiers digital. Class D can also use Sigma/Delta modulation, but I'll let that pass for now. In Class D the music signal is modulated on a very high carrier frequency that can be easily filtered out, together with the neccessary smoothing of the chopped signal to recreate a nice gentle waveform.
This method is very different from regular class A/B, where there is (explained in simplified form) a power transistor that is fed by a low voltage signal on one leg, a huge power reserve on the second leg and the speaker on the third leg. The input signal is merely amplfied. The transister is continually varying its output voltage.
Of course, there are exeptions to the rule. Sharp for example has made an integrated amplifier that has digital inputs, and digital volume control and Tact, now Lyngdorf Audio, also has a completely digital amplifier, although the speakers are fed an analog signal of course. Lastly, the B&O modules are also available with digital inputs. But these still operate in an analogue fashion.
Here are some indications regarding efficiency. The number are mere indicative, not absolute, but you'll get the picture.
Class A = 25% efficient.
Class AB = 50% efficient
Class D = above 90% efficient
Class A always consumes the same amount of power and to output 40 watts into a hungry speaker it would consume about 100 watts from the mains. Because class D draws less current from the mains, a much smaller transformer can be used and a lot less heat is produced.