Why gun caliber does not define a battlecruiser

Does gun caliber show whether a battlecruiser sits nearer the battle or cruiser end of the spectrum?

Not reliably; navies often reused contemporary battleship guns for economy, so role and overall design matter more.

Operational role is a more meaningful classifier than weapon size. Designers often selected the same gun already being produced for contemporary battleships because common manufacture was cheaper and simpler. A large caliber therefore need not prove that a ship belonged in the battle line. Speed, range, protection, structure, and intended employment remain more revealing than the main battery by itself.