as mr audioguru mentioned, class b amps have a terminal of each (push & pull) transistor shorted together, could be emitters or bases depending on the configuration, with the inputs coming off a center tap transformer. while a class ab will have some components (diodes, resistors) providing bias to move the q point off zero, eliminating zero crossover distortion.
Center-tapped driver transformers have not been used in audio amplifiers for 50 years!
The output transistors are a complimentary pair. One NPN and the other PNP.
They are both emitter-followers and have their emitters connected together or each has a low value resistor in series with its emitter.
When their bases are shorted together then they don't conduct any current when at rest. So it is class-B with horrible crossover distortion in the "dead" center of the waveform.
When the transistors have two diodes in series between their bases then they always conduct a little so the waveform flows smoothly from one transistor to the other in class-AB.
While not much in the audio spectrum, push-pull amplfiers are still around, in the higher power applications ... even those using center tapped transformers.
Althought not in commercial service, there are push-pull parallel circuits used in other applications to achieve higher power levels.
Class A, AB1, and AB2, B, and C are still characterized by the current flow during quiesence or the current flow during the input cycle.