9 mm Luger designation to avoid confusion with WHAT other 9mms?
It was introduced with the 1902 "fat barrel" Luger pistol, apparently not seen in the USA til 1903 and adopted by the German navy in 1904. The German army did not catch up til 1908. (Still another name for the round, 9mm '08.)
The 9mm Browning Long dates to 1907, I think, the 9mm Browning Short/.380 to 1908, the 9mm Bergmann Bayard to 1910, and the 9mm Steyr to 1911.
The Para was first. No confusion possible for a while. Careful naming became necessary because of the competition.
It's not that there is no logical system of cartridge and caliber nomenclature, it's just that there are several and you have to learn which you are looking at.