@MrsMouse
The "incomplete" swing comes from the 0.02 seconds (200 milliseconds) the batter has to make the decision to swing and where. They start to swing and the ball movement tells them to "stop" their swing mid-process.

Not easily done.

@MrsMouse
If the ump judges the pitch went through any part of the strike zone and the batter didn't swing, that's also a strike.
If the batter hits the ball, but it doesn't stay in play, that's a foul ball. The first 2 can be counted as strikes, but it isn't an out, unless the full is caught by the opposition. Only a swing with no contact or a pitch called by the ump without a swing can lead to an out.

Let me know if I helped or am now the butt of a joke

@MrsMouse
I'm incapable of separating a joke from a sincere question. I'll try to explain in case you're serious.

If the batter swings and makes no contact with the ball it's a strike. Swing and a miss. Did the batter make a complete swing? Ump call.

If the pitch doesn't go over the plate and is thrown between the batter's knees and chest (the strike zone) that is a ball by judgement of the umpire, as long as the batter didn't swing ( see above.) Only 4 ball are permitted per batter.