Here are links to two recipes for key lime pie, which I love but as of this writing I haven't tried these. One recipe is from Serious Eats and the other from America's Test Kitchen (ATK).
There's a big controversy over whether you need to use actual key limes or ordinary "Persian" limes for key lime pie. The Serious Eats recipe below is adamant on key limes, but the America's Test Kitchen recipe is written for regular limes and says key limes are optional. True key limes are round and very small, about the size of a ping-pong ball, and can be hard to find, plus it takes a lot to provide enough juice. The Serious Eats recipe below calls for 1/2 cup of juice and says about 20 key limes, whereas the America's Test Kitchen recipe calls for 3/4 cup of juice and says about 18 limes ((if you're going to use the optional key limes). This type of contradiction is pretty normal for recipes. Anyway most of what I've found says yes, there will be a difference in a pie using Persian limes instead of key limes, but the difference is not really that great and even if there is so what - both pies will be delicious, just not the same. No one expects, for example,, a rhubarb pie and a strawberry-rhubarb pie to be the same. I notice in the comments on the Serious Eats recipe, which calls for key limes, that most people used Persian limes anyway but still said it was delicious.
These two recipes are almost identical. The ATK recipe says it is based on "what many think of as the go-to recipe for key lime pie filling: the one on the back of the bottle of Nellie & Joe's Famous Key West Lime Juice." I'm assuming this "famous" recipe is a standard, and both of these recipes started with it.
America's Test Kitchen Lime Pie
ATK is a subscription website. This is actually on their Cook's Country website (ATK is a mess of confusing and stupid related websites). This recipe is almost identical to the Serious Eats recipe. It uses a meringue topping instead of simple whipped cream, which I don't think is really an improvement. It also has a slightly different graham cracker crust, because it includes pulverized pretzels for sturdiness and buttery saltiness, which I do think sounds pretty good.