Biscuit (British) = Cookie (American English)
Same difference many of us call the treats we give our dogs cookies when the package calls them biscuits.
Soon the Brits will all be sitting naked in a circle of soft sand, wondering where their next meal will come from and how they will eat it if it comes.
I wouldn’t say that cookie=biscuit, but that a “biscuit” (in English) is a certain type of “cookie” (in American).
In an American grocery store, you will find “tea biscuits”—that’s more like what the Brits mean by “biscuit.”
I don’t think, even in England, that anyone would call a big, soft, gooey chocolate chip cookie a “biscuit.”