TSFS was originally supposed to include Romulans. The producers at some point said, "who ever heard of Romulans," so they changed it to Klingons. They didn't bother changing the ship.
There was some business some time later about it supposedly being a stolen Romulan ship, but that was dropped.
Memory-Alpha, and every other later-created resource, including the later tv series and films, twist every which way to retcon TOS to account for their mistakes. TOS stands on its own.