German GECO catalog 1937, p.54:

Amerikanische Original-Patronen
(Original American Cartridges)
...
Kal. .25-35
Diese Patrone ist auch in deutschem Fabrikat unter der Bezeichnung Kal. 6,5x52R lieferbar
(Cal. .25-35 /pictured is a specimen by Remington/
This cartridge can also be supplied in German make under the name of cal. 6.5x52R)
...
Note: translated from German by myself

So in my modest opinion these two cartridges were considered practicaly the same and interchangeable up to WWII and probably decades beyond, till CIP decided, for reasons presently unknown to me, to make/declare/recognize them as two distinctly different cartridges.

With kind regards,
Jani