In WW1 battle cruisers had battleship guns, armor between cruiser and battleship and cruiser speed. By WW2 battle cruisers had battleship armor, cruiser speed and guns between cruisers and battleships.
In my reading of history, I do not find much from navies other than the RN that pursue the model that a battlecruiser was a ship with battleship guns, less armor, and cruiser speed.
Even in WW1, the Germans "battlecruisers" seem to be a class of sub-battleships -- ships with reasonably balanced designs, with guns and armor that are more than cruisers but less than battleships, with more speed than battleships.
I think the determining issue is the pursuit of speed. A battlecruiser was a capital ship with speed that was in the range of a cruiser. Battleships proper, of that era, were substantially slower. How the increased speed of the battlecruiser was achieved differed between nations -- whether by going full battleship armament and size but reducing the weight of armor (the British approach), or by taking a battleship style design and reducing the whole package in a scaled and balanced approach (German approach).
This latter approach seems to be the path pursued by the French with their battlecruisers (Dunkerque and Strassbourg). I don't know enough about the original design of the USN's Lexington, but the WW2 era Alaska clearly was more to the German model of battlecruiser than the British model.
The British applied the label of "Pocket Battleship" to the Graf Spee (the Deutchland class). They didn't fit the British model for a battlecruiser. The Germans never called them battlecruisers either. They called them armored cruisers.
The Japanese Kongos were British designs, and followed the British model of battlecruisers. Did the Japanese identify them with a term similar to "battlecruiser", or was that a western-applied label? I know by WW2 they were considered battleships by the USN.
By WW2 it appears that the British concept of the battlecruiser was absorbed by the concept of the fast battleship. Once you have a KGV, a Bismark or North Carolina (much less an Iowa), what room is left for a ship of battleship armament that sacrifices armor for cruiser speeds. All that was left, then, was the niche of the ship that was bigger than a cruiser but smaller than a battleship, of the model of the Dunkerques, or the Alaskas, or the (gulp) Scharnhorst and Gneisenau.
-Mark
(aka: Mk 1)
