That cartridge was marketed and referred to in contemporary catalogues by several names.

Brits tended to refer to is as .375 Nitro Express Rimless, .375 RNE, .375 Nitro 2.25"... .

Other references were 9.5X57, 9.5X56, 9.5X56.5... .

It is worthy to note that catalogues of the day often listed both .375 Nitro Express and 9.5X57 with a powder charge two grains heavier for the 9.5 than the .375 RNE though both had identical dimensions and projectiles.

There is disagreement about whether the cartridge originated with Westley Richards ca. 1908 or was of Austrian origin.

DWM531, from 1939 Stoeger

Note the Mannlicher Schoenauer 'action'.

ICI / Kynoch