I admit, the situation is very complicated, even if only looking at the M88.
The 7.9 mm Patrone 88 used an average bullet diameter of about 8.06 mm (.317").
After learning of the new French balle D, the German military in 1903 decided to replace the M88 round nose bullet with a much lighter pointed bullet, designated S for Spitzgeschoss.
When copying the new French invention, not only the pointed nose was copied, but also the larger bullet diameter. The new S bullet has a maximum diameter of 8.2 mm (.323").
Now comes the difficult part. Like the French, the Germans kept the bore dimensions UNCHANGED. This was possible, because the groove diameter of the Gewehr 88 barrel already was 8.2 mm (the French was 8.3 mm, identical to the diameter of the new balle D). The original M88 round nose bullet had had a diameter smaller than the M88 groove diameter (just like smaller diameter French balle M).
But the new bullet, while fitting the bore, required a new, wider case neck. So what was changed in the 1903/1905 time frame, was re-reaming the chamber shoulder and neck of all M88 and M98 rifles in the military inventory to acommodate the new S case. Let me repeat again: military barrel bore dimensions were not changed.
Enter of the German gun trade, because contrary to France, everyone who had the money (a hefty sum was needed) could freely buy a German military 7.9 mm rifle and its ammunition. Particularly hunters did, Kaiser Wilhelm II being the most prominent example. But the gun trade now started to build rifles with tighter barrels (8.06 mm groove diameter), appropriate for the old M88 bullet diameter. It looks as if most hunting bullet manufacturers used this diameter, not that of the new S bullet. (The case standardized by the commercial manufacturers in 1906 had the dimensions of the old M88 case. No bore dimension standardization existed.)
This resulted in the co-existence of two commercial “8 mm” cartridges on the German market with different bore diameters but no clear distinction namewise.
In the 1920s, the German gun trade and industry agreed to give the smaller groove diameter barrels of commercial origin the name 8 x 57 J and the barrels with larger bore dimensions 8 x 57 JS. The J in both cases stands for infantry (J for I is another story) and the S for S Patrone dimensions.
Gewehr 88 and Gewehr 98 (Mauser design) as originally issued(!) fired the Patrone 88. In modern terms, they had a 8 x 57 J chamber, but the bore dimensions of 8 x 57 JS. After the adoption of the S cartridges in 1903, the chambers of all rifles in the inventory were re-reamed to 8 x 57 JS.
In short, we have the 8 x 57 JS with identical dimensions as the military 7.9 mm cartridge (bore since 1888, bullet diameter since 1903). And we have the tighter bore 8 x 57 J, which uses bore dimensions invented by the German gun trade, based in the old Patrone 88 bullet diameter.
I consider this 8 x 57 J as invented by the gun trade as a dead end from the starting point. But the anomalies created by the Versailles treaty enabled it to survive, because civilian ownership of the 8 x 57 JS after 1918 well into the 1930s was illegal, because it counted as war material.
Now, this is the story behind the first column of your table. I am not really in a position to comment on the other columns.