Class A single ended output, the form of audio amplification that does not altering the signal in a significant way. In a Class A amplifier the output operates in the center of its operating curve. In the center of the curve the output draws half of the available current. Signal swings current up and down from the center point. It is essentially a linear system. Signal is amplified without manipulation or processing. Distortion characteristics of single ended Class A amplifiers is primarily even order harmonics with the second harmonic being dominant. These are musical harmonics. Virtually all digital audio formats use some form of compression to save bits and bandwidth removing nuances that give audio life. Some of the nuance removed in digital compression includes harmonic content. Harmonics give music depth, regardless of claims that they are too low to be heard harmonics are a key ingredient of music. Using a Class A analog amplifier as the last link driving your speakers will in effect replace harmonics removed during digital compression processes.
Push-pull Class AB manipulates by splitting the signal in half through a phase-splitter. Each half of the signal is amplified through separate output stages. Since it is half, either positive or negative an output stage can be biased off for part of the cycle. The output draws less current and runs cooler. The output stages merge the two halves of the signal back together. In a transformer coupled amplifier the merging is done in the output transformer.
As you might imagine in order to amplify without altering the signal both halves of the split signal must be amplified exactly the same. Even if component values are a tight tolerance there can be some difference between the signal halves. As components in circuits age differences can get worse. An artifact of push-pull Class AB is cancellation of the most desired second harmonic, but leaves the least desired third harmonic distortion content. Even if you bias up the push-pull to Class A operation you still have artifacts from phase splitting. If you are going to run push-pull Class A, you will not save on power consumption. For Class A higher output better performance is optained operating two output stages parallel single ended.
Class D modulation techniques encode information about the audio signal into a stream of pulses. A common modulation technique is pulse-width modulation (PWM). PWM modulates the input audio signal to a triangular or ramping waveform that runs at a fixed carrier frequency. This essentially creates a stream of pulses riding a fixed frequency carrier. During each period of the carrier the ratio of the PWM pulse is proportional to the amplitude of the audio signal. The duty ratio within individual periods is either 0% or 100%. The output stage uses a switching technique where current is switched on or off depending on the duty ratio. An LC (Inductive Capacitive) filter is used to remove the carrier frequency leaving the audio signal in the form of current controlled by the switching output stage. Alternatives to PWM include pulse-density modulation (PDM) where the number of pulses is proportional to the average value of the input audio signal.
The more detailed Class D Amplifier PDF link below was put out by Eric Gaalaas of Analog Devices in 2006. It's dated, but should be basically valid. Clearly Class D amplifiers are not linear analog amplifiers, they are more akin to an analog to digital/digital to analog system.