I cannot tell about Teschner and Collath. I think they were very inventive and used to do things their own way. So it is possible that their 8x72R was a bit different.
Hunting cartridges were standardized around or before World War I, so dating the rifle may also give clues.
In the end it will not matter: there is no modern factory ammo available, you have to reload.

The Dynamit Nobel handloading book says:
"probably several designers have worked on development of the 8x72R, which appeared the first time in 1898. But without doubt the cartridge can be attributed to Wilhelm Brenneke. The reference to Sauer & Sohn, which is found in literature, is probably not correct: there was a cartridge 8x72R S&S, but this is a necked down 9.3x72R S&S and not identical to the conical 8x72R case. The 9.3x72R S&S has a slight bottleneck and is not identical with the conical 9.3x72R which was the starting case for the 8x72R".

Reloading data in the book give a muzzle velocity of max. 680 m/s with a 12.7 gram jacketed round-nose bullet from RWS (definitely .318). Max. pressure 2500 bar.

Fuhrmann