A "plate appearance" refers to any time a batter comes to the plate and completes a turn at bat, including walks, hit-by-pitches, and sacrifice hits, while an "at bat" only counts when a batter is put out or reaches base via a hit, fielder's choice, or error, excluding walks and sacrifice plays; essentially, a plate appearance is a broader category that includes all at-bats, but not all plate appearances are considered at-bats.

In some cases, a pitcher may decide to deliberately walk a good batter. For instance - it's two outs, there are men on second and third, a powerhouse hitter comes up to bat, and a weaker batter is behind him in the rotation. The pitcher will deliberately signal to both the batter and the catcher that they are going to give him a deliberate walk, hoping that he could then force the follow-on batter to pop out. It happens often enough that this is not considered an at-bat.

A baseball fan for 65 years and I’m still learning.

I'm sure you've seen or heard OBP, on on-base percentage.
Since this includes getting on base by walk or hit by pitch, those get added to hits for the numerator.
Plate Appearances, not at-bats, are used for the denominator.
So, Plate Appearances are actually used in the calculation of an important stat.
If they didn't, a guy who walked 90 times would see there OBP 150 points higher than the batting average. But, the 90 gets added to the denominator, too.
To whit:
Say a .300 hitter has 600 at-bats. 180 hits. Now, let's say that guy walked 90 times.
He reached base 270 times. With 600 at-bats, his OBP would be .450.
Instead, that 270 times reaching base is divided by (600 at-bats + 90 other plate appearances), or 690 PA. The OBP would be .391.
Now, having an OBP 30% higher than the average is really good, but it's not .450.
Rose walked about 1,560 times. That's 60 something per year, which is good, but not great.
That's why his batting average is tied for 137th all-time but his OBP is 240 something on the list.
He didn't get on base often enough to push his all-time OBP into the upper stratosphere.

So Math Geeks run Major League Baseball. I do appreciate your time and effort Professor. Truly love the game. And now I find out I don’t have to think about it, just watch. The Phillies are in IT. So I’ll be wrapped around the axle for awhile.

A problem comes in, however, when stats people use indexes and then misunderstand the leverage these exert on winning & losing
An example is WAR. The 3 biggest proponents of WAR don't even calculate it the same way. And, they are all guilty of weighting (better termed "fudging&quot things by adjusting until guys like Ruth, Bonds, Mays, Aaron rose to the top.
And, in examining the calculations of WAR, lots of statistical experts & mathematical modeling people (like me), there are several *what the heck are they doing this for" moments.
Yes, the math geeks are running baseball. It doesn't mean they're doing ut right, despite the lovely story we saw in Moneyball.