They aren't. Roman ships are Warbirds
The likely reason behind why the Klingons and Romulans have similar names is that at one point the two empires were allied. Both sides engaged in a technology exchange causing some to believe that Romulan cloaking devices may be linked to early Klingon design.
There are both Romulan and Klingon Birds-of-Pray, as well as both Romulan and Klingon Warbirds. They are simply classes of ships that share some similarities. Compare it to twentieth century Earth... navies from many different countries have destroyers, frigates, carriers, etc...
The real OOC historical reason is that the Klingon Bird of prey was originally in Trek 3 intended to be a Romulan ship, stolen by the Klingon Captain. while this was changed, the termology became a hold over