They call Orions destroyers because GTB looks like a bomber and GTC was a cruiser. Their lettered designations just weren't up to the task. They realised this themselves, as FS2 has many 4 letter designations, as the 3 letter system was too restrictive. It all makes sense, regardless of how stupid it is.
EDIT - 'Battleship destroyers'? Are you on crack?
'Destroyers' are an evolution of pre-WWI 'torpedo boat destroyers' used for escort, armed with smaller, quick firing weapons to kill - you guessed it - 'torpedo boats', which were small, fast torpedo armed ships. Battleships of the time could not engage them, as they were armed exclusively with large, slow firing weapons. Basically, the battleships were threatened by the cheap and nasty Torpedo Boat Swarm (TM), so they were protected by screens of Torpedo Boat Destroyers.
Later DDs gained more roles (ASW, AA area defence, etc) and they were simply termed 'destroyers'. The term comes down to us from a far simpler age.