I've been researching my 4" Kriegsmarine U-Boat deck gun shell casing and can say without a doubt that "metric vs inch vs actual projectile diameter" is not as cut and dry as you'd think. The throat on my shell is 4.06" the projectile is listed as 10,5 cm. According to various WWII literature converted to PDF, Germans referred to their gun bore sizes in very rough terms. My shell is technically a 105mm, but is commonly called a 4". So don't get too hung up on sizing nomenclature, it's relative to country of origin, language, service branch, etc as to what a shell was called...
Russ