I look at "turn over" and "crank" as the same thing, as long as the crankshaft is truning, the pistons are moving up and down in the cylinders and the valves are opening and closing it is "cranking" if the spark plugs are firing and the engine continuues on it's own (the starter is no longer keeping the crankshaft spinning) then the engine is "running".
Holding the gas pedal hard on the floor and truning the key to the "start" position will "crank" the engine but it will NOT "start". As soon as you let the pedal off the floor the injectors will start to work again and it will start. However I recomend you stop cranking the engine, then take your foot off the throttle, then crank it again otherwise you might wind up with the engine at 4-5000 rpm on a cold engine.