Umm, a key lime is a particular variety of lime. Just like your persian lime is a particular variety of lime.
They are not the same.
You are not making key lime pie.
And most folks can’t tell the difference, so ultimately, only the purists care. I guess I am one, come to think of it, and I’d be happy to announce that we’re having persian lime pie for dessert - a conversation starter.
I know the difference and have used both real key limes and persian limes. I use key limes when I can find them growing around the neighborhood, but I’ve found that persian limes come close to tasting like key limes when the whole lime is juiced including the rind - and that’s the key (pun intended). Besides, I live on Sand Key, so, as I say, I make Sand Key Lime Pie (wink wink).