I learned it this way:
Peter Piper picked a peck of pickle peppers.
A peck of pickle peppers Peter Piper promptly picked.
If Peter Piper picked a peck of pickle peppers,
where is the peck of pickle peppers Peter Piper picked?
A "pickle pepper" being a kind of pepper, like a "canning tomato" or a "baking apple."
A regional difference in the rhyme, perhaps.
Here's another one:
All around the (fill in the blank) the monkey chased the weasel.
I learned "mulberry bush" but I've also heard "cobbler's bench," "vinegar jug," and "flagpole."
Lindy