What is the difference between differential rail-to-rail, push-pull rail-to-rail and rail-to-rail OPAMPs
A differential op-amp has two outputs, one that works the usual way, and another whose voltage goes up when the main output goes down and vice versa. They are useful for driving differential ADC inputs, driving differential transmission lines, etc.

A push-pull output op-amp is the usual kind, whose output is capable of both sourcing and sinking current. Probably many of the ICs that aren't labeled with this feature have it anyway. For the devices where it's mentioned, somebody probably thought these op-amps might be listed in the same selection table with comparators, since many comparators have open-drain outputs and aren't able to source output current.