Hmmm... Had a longer post but lost it, and decided it wasn't worth it.
Single-ended can be class A, B, C, whatever. A differential design ideally cancels even-order harmonics, leaving odds dominate. This provides lower distortion, but odd harmonics generally sound "raspier" to us so in fact a SE design with distortion dominated by the second-order term may sound better even though it actually has higher distortion. SE designs are most often biased class A (I am not sure I have seen an audio design that was not), meaning "full" current flows through the device always.
Push-pull I have seen used two ways. In the first, and the way I use it, it describes an output stage that typically uses complementary (or two out of phase) devices so one sources current (pushes) and one sinks it (pulls). Again, these can be biased in class A, AB, B, C, whatever. Because currrent flow switches from one device to the other, there can be distortion as the signal crosses over from say the source (+) to sink (-) device. For this reason you rarely find class B audio amps (and never class C IME); they are usually AB so a small amount of current always flows through both devices to reduce crossover distortion.
The other way I have seen push-pull used is to describe a differential circuit, but that was not how I was taught/weaned.
I don't think any of this disagrees with previous descriptions but I did not read closely; different ways to describe the same thing.
