And basically, keeping in mind a batter gets 3 strikes per at-bat, a foul tip is considered a strike, regardless of whether the catcher catches it or not, except for situations where it would be strike three. In that case, the catcher must catch the foul tip for it to be a strike.

The reason I was asking was because cricketing batsmen don't have to run when they hit the ball. They often offer fairly static shots (little or no bat swing) and sometimes edge the ball to the wicketkeeper or slips (ancillary fielders behind the batter assisting the wicketkeeper). Also wicketkeepers stand well back when fast bowlers (pitchers) are bowling but stand up close when spinners (slow bowlers) are bowling. Catchers always stand (ok, squat) seemingly millimetres from the batter.

They take those catches!!!??? I'm genuinely impressed!!!

I really should spend a little time on YouTube and Wikipedia boning up on it. And yeah, catcher is a brutal position. It's enormously hard on the body. But, he really is kind of the field general, telling the pitcher what to throw and where, helping direct positioning of the fielders, etc.