Cecil’s response here, even though this is a “classic”, is way off the mark. The etymologists consulted must have given him a bum steer.
Outside of the USA, the word for the number of levels in a building is storey, with a plural of storeys. As with a great many English words, it was probably brought over here intact, but mis-spelling over a couple of hundred years has caused the “e” to be dropped.
The original column, Why are the floors of a building called “stories”?
Etymonline.com, probably based on the OED, pretty much agrees.
What difference it could make whether the spelling is otherwise story or storey is something I can’t answer, meaning that I can’t figure out the OP’s point at all.