Bird of Prey has always been the Klingon ship. Warbird has always been the Romulan ship. I am pretty sure this is the first time I have ever heard a Klingon Bird of Prey called a Warbird. Never watched much of Enterprise, so I didn't know that the mistake had been made at least once before. Of course there is a difference between an episode of a tv show and a big budget feature length film. I have a feeling that from now on they will be called Klingon Warbirds. Why? I dunno, but I am pretty sure the official reason will simply be, "Nero did it".
Another dumb continuity error (NERO DID IT!!!) is that they mention the Warbirds decloaking in during the simulation. Yet in TOS I seem to remember them making a huge deal about the discovery of the Romulans' ability to cloak their ships. Why would they have been so shocked and awed at the very idea of Romulans having cloaking devices, when they already knew the Klingons had that technology? And why were Kirk and friends so intrigued and confused by the cloaked Bird of Prey in Trek III? Perhaps Klingon "Warbirds" with cloaking devices are pretty standard, but a Romulan Warbird or a Klingon Bird of Prey with a cloaking devices is absolutely unheard of.