Officially, a cruiser that burns like a Battleship is a "Large Cruiser", regardless of gun caliber. Stalingrad, Agir, Alaska, Harlem, JohanDW, and Gouden are all "Large Cruisers".
Personally, when a cruiser that burns like a battleship ALSO has large caliber guns, I tend to refer to them as "supercruisers" like much of the community does, but this is a colloquial term used by the community and not the term World of Warships uses to denote a cruiser that burns like a battleship.
Possibly, but not officially yet. CB in naval parlance refers to "Large Cruiser", while CC refers to "Battlecruiser", but we do not use it internally the way we use CL, CA, BB, CV, DD because we are trying to keep things less complicated in this manner. That does not mean, however, that it cannot change in the future. If enough Large Cruisers are in the game to the point where being designated CB instead of CA is deemed more helpful than confusing, it may happen. ...
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