Pushing the pedal did three things:
1) it "primed" the engine by using the accelerator pump to spray some fuel in
2) it set the automatic choke
3) it set the idle to high, via the high idle cam.
Fuel injected systems control the engine's starting fuel needs by computer.
Eraser gave an excellent description of a majot difference, being that pumping the pedak before turning the key does nothing on a fuel injected car but open and close the throttle plate. The computer in an injected car takes a signal from the engine temp sensor, and based on that combined with the other sensor inputs it
1) richens the mix (makes the injector pulsewidths longer) and
2) by passes the oxygen sensor circuit, to allow the engine to run rich,
In short, in a carburated engine everything is operated manually by linkages. Pumping the pedal sprays gas into the engine and sets the chok & idle for cold operation.
In an injected engine, all of its fuel comes from the injectors. The injectors stay closed when static and only open when a signal tells them to. Thus, when the kay is "OFF", there's no signal, the injectors don;t open, and nothing happens.