7.92mm is closer to 8mm than it is 7mm, so that is why the 7.92X57mm cartridge is called the 8mm Mauser.
The 7mm is actually 7.21mm, closer to 7mm that 7.92, so it is called the 7X57mm Mauser.
The 57 is the length of the brass casing in millimeters, the brass is 57mm long.
The 7x57 and the 8X57 ARE NOT INTERCHANGEABLE!!!!!
7X57mm = 7.21 mm Diameter bullet(.284") with a case of 57 mm length.
8X57mm = 7.92 mm Diameter bullet(.323") with a case of 57 mm length.
If you run across a cartridge that says 7X57Rmm, the 'R' stands for a 'Rimmed' type cartridge, the base of the cartridge is wider than the body.
You will also see 8X57mmJ, 8X57mmI, 8X57S and 8X57JS...
In 1888 the 8X57mm was born and it utilized a .318" diameter bullet; around 1905 the bullet diameter was changed to what is used now, the .323" diameter bullet.
The J and I denotes 'Infantry' ammunition as loaded for the German army.
The S denotes the use of the larger(.323") bullet. The J and the S have stuck and is used today in the United states and Europe.
The most common 8mm Mauser ammunition around today is the 8X57JS or the 8X57J. Most of this ammo is corrosive, and some of it is pretty harsh, so be sure and clean your gun after shooting any of this corrosive ammunition.