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156/14 is the old german caliber stamp used until 1911 to indicate the caliber.
Its just an fluke that it is the same with an bullet weight.
As you see in the list for the proofing was used an 17,1 gramm bullet.
The list gives an bullet weight from 13,1 gramm for the usual ammunition.

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Right in part only. The gauge numbers did not indicate the groove diameter, but a diameter between the lands only. It was measured at the proofhouse using cylindrical plugs. The largest number that passed the barrel was stamped. There were no intermediate steps from gauge number to gauge number. Here a # 156.14 = 7.87 mm = .310" plug passed the barrel. but a # 141.96 = 8.13 mm = .320" one did not. So the actual bore/land diameter of a Barrel marked 156.14 may have been as large as 8.12 mm = .319".
The powder charges and bullet weights for preliminary proof, final proof and service load in the 1892 tables were for black powder proof using cylindrical lead bullets only, in no way related to the then evolving, new smokeless cartridges.
In 1893 a new proof rule for rifles using the M88 8x57I cartridge was installed: The Spandau arsenal produced a special smokeless proof powder: Used at the same charge weight as the then military flake powder behind the regulation 14.7 gramm = 227 gr bullet, it produced a 4000 atmospheres pressure, a 33% overload in this cartridge. Soon the proofhouses used this powder for other Nitro rifle cartridges too. Rifles proofed this way were not marked with the familiar eagle + BGU marks, but with a big crown + a small crown over N. This smokeless proof was sometimes used by the Suhl and Zella – Mehlis proofhouses until 1923. (Oberndorf / Mauser proofhouse did not use these marks on their commercial M98 action rifles. As those were offered only as rifles and only for smokeless cartridges, they deemed it superfluous to mark them other than crown/B = proof load fired and crown/U = viewed for defects.)
The 8x50R Mannlicher then used a long, heavy 15.8 gramm = 244 gr .323" bullet in a .313" land, .329" groove diameter barrel, depending on the long bullet setting up from the sudden blow of the fast burning, high pressure Austrian smokeless powder.

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