I suspect the original European nomenclature for the .25-35 Winchester is incorrect.
Here in Canada when we reload a 25 calibre rifle cartridge (250-3000 Savage, 25-06 Remington, examples), we use .257" diameter bullets.
When we reload a 6.5MM rifle cartridge (260 Remington, 6.5x55 Swedish Mauser, examples), we use .264" diameter bullets.
These bullets match very closely the groove diameter of the barrel, not the bore diameter.
The British are the main "offenders" in this area, naming their cartridges using the bore/land to land dimension in the cartridge name. Thus their .303 British cartridge uses a .311" bullet, while their .275 Rigby (aka 7x57 Mauser) used a .284" diameter bullet.
Hope this helps.