I see "pie plate" referred to as a target grouping quite a bit and thought it referred to a 8-9" pie pan sized target, about the same as a paper plate.
I think if you look at both the waistlines
and the targets of the typical online commentor who is bragging about "pie plate sized groupings" you'd understand why they think a full-size paper plate is a "pie plate". The people who are bragging about picnic-plate-sized groups with a rifle are probably the same inbred, sloppy, neanderthal behemoths you see doing all those "bump-fire" videos on YouTube.
In the strange world of dinner-setting parlance, a "pie plate" is formally called a "dessert plate". In a standard place setting of china, it is the next-to-the smallest plate--the only one smaller is a saucer (which is the one you set your coffee cup on). A typical "dessert plate" is generally smaller than 6.5" across. This is just big enough to fit a 1/8 slice of pie, or a polite portion of cake, or most formal desserts...
That's a MUCH smaller circle than a standard-issue paper plate, or dinner plate.
And unlike a 9" circle, a "pie plate" grouping at 100 yards is actually something to brag about--for someone who isn't using a scope, or isn't a "professional"...
I've shot "picnic-plate" sized groupings at 100 yards with stranger's M1 Garand using 50-year-old Greek surplus ammo and iron sights, and to be honest, I was actually ashamed of my performance. If I can't cover a 6-shot string with the base of a pop can, I consider it to be a total failure...
In the competition rifle world (and among military sharpshooters), when they are shooting at 100 yards, they talk about quarter or dime-sized groups, just as a point of reference...