Class A push pull is mid biased ... as one transistor swings toward saturation, the other swings toward cutoff.Class AB transistor amplifiers are always biased to the mid point otherwise they would not work correctly. Class A transistor amps are just class B (or AB) biased to have a large current flowing in the output stage in the quiescent state. A class AB would have the same output stage topology but would be biased so that the output stage passes just a couple of mA in the quiescent state.
Class B is by nature, push pull as they are biased exactly at cutoff as one transistor swings toward saturation, the other simply remains in off state while waiting it's turn.
Class AB is the same as class B, only it is biased slightly above cutoff in a bid to eliminate the need for meticulous bias generator adjustment.
Beyond this region of overlap, they run class B ... a transistor swings toward saturation, the other waits it's turn in off state. If it didn't, it's just be a class A.