Well that's on the right track, but not quite there. Stereo just means two channels of amplification, of course. Each channel might be single-ended or push-pull. The single ended topology can use any number of tubes in parallel (one per channel sounds best, though). In a single ended amp, the plate DC voltage goes right through the primary windings of the output transformer, and the output tube(s) amplify the whole (music) AC signal waveform, positive and negative voltages. The HV DC load on the output transformer is why one either needs big-butt, airgapped output transformers, or limits oneself to low power.
In a push-pull amp, there's a phase splitter ahead of the output tubes that separates the AC signal into its positive and negative components. These are amplified separately by two output tubes (or even numbers of paralleled tubes, as above) -- thus one tube 'pushes' and the other 'pulls'. The big advantage is this: the plates of the two output tubes are connected to the 'ends' of the primary winding in the output transformer and 'push and pull it with AC. There's no DC superimposed on the AC signal, so the transformer can be smaller and operate more efficiently... and in practice output power can be much higher.
Class A and Class B (and the hybrid Class AB) refer to the operating points of the output tubes. SE amps are USUALLY Class A (danged inefficient, but sounds great), but they don't have to be. PP amps are USUALLY Class AB (be they solid state or tube amps)... but there are a number of big, hotrunning, low-powered Class A SS and tube PP amps out there.
Next class, we'll talk about negative feedback...