Different countries used different naming conventions, and sometimes they changed within a country over time, so you are correct, it can be confusing.
Most collectors will refer to large caliber (“artillery” as opposed to “big bore African game calibers” or the like) by the bore diameter of the gun and the overall length of the case (in millimeters) and indication if it is rimmed, semi-rimmed, or rebated at the base.
For example, a WW2 40mm Bofors case would be called “40 x 311mmR” regardless of who made it, and the 40mm Bofors was used by nearly every country in WW2. Sometimes it is referred to a “40mm/L60” indicating it is the 40mm gun with barrel 60 times the bore diameter, to quickly distinguish it from a post-WW2 40mm Bofors gun “40mm/L70” with a barrel length 70 times the bore diameter which uses and entirely different 40 x 365mmR case.
The best reference for this sort of ammunition is Robert Hawkinson’s outstanding “A Guide to the Identification and Research of BIG BORE AMMUNITION 20mm to 80cm” which has three section. The first lists virtually all known cases sorted by ascending case size; the second by country and ascending case size; and the third section is a listing by bore diameter and case length (or if a bag type gun) and the country and gun type which used them. He also lists the rim diameter, and shape of case (straigh,t/tapered/necked) and case material (brass/steel) and if a “fixed” or “separate loading” round.
Price was $110.00, but a bargain for the info it contains, and the price may have changed. I heard that he only has four copies of this book left and anyone interested in this stuff really needs to get one. Contact Robert Hawkinson rcjctg [at] aol.com
Otherwise, you are left to research each case by trying to guess the country, and then look up their artillery pieces in the caliber indicated by the markings or the mouth diameter and seeing if you can find something that lists the case length or markings. That is the hard way to research artillery cases!