I think the difference here is live-ball strike vs. dead-ball strike. If the pitcher hesitates because the batter stepped out with both feet (b), then we have a dead-ball strike. If (a) or (c) occurs, you have a violation by both the batter and pitcher and you wind up with a "re-do." If, by stepping out with one or both feet or holding up a hand to request time (a, b, or c), the pitcher is not affected and he delivers a legal pitch, that pitch is to be called a strike irregardless of the pitch's location and the ball remains live.
BTW, you cannot get two strikes on this play.
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