There's a pretty decent write-up of the "Normalization" process that occurred in the German sporting ammunition industry in Dixon's "European Sporting Cartridges" vol 1, page 126. The first line is a good summary:

"A major problem with the number of companies producing cartridges in Germany was that many introduced their own types similar but apparently non-interchangeable with those of other companies."

The luxury of well-defined and fixed dimensions of cartridges as we have presently in the US just didn't exist in Germany before 1900 and the German ammo industry struggled to address this even through the post-WWII years, various cartridges being "Normalized", or set to standard dimensions, at different dates. According to Dixon the 8x60 was done sometime before 1923. The question of "J" -vs- "S" bore 8mms is separate from this as both needed standardized dimensions.

All this aside, GDU has it exactly right in that only a chamber cast and bore slug can tell you about any particular rifle. Thank goodness that's easy to do and there's brass available for just about anything these days!