I believe that 7,92mm refers to the bore diameter. And 8mm refers to the groove diameter.
The 7.92x57mm is the same as the 8mm Mauser. The original 8mm Mauser featured a .318" round nosed bullet. And around 1905, the Germans came out with the first spitzer bullet. They increased the bullet diameter of the new load to .323". They called this new loading the "7.92x57 IS". "IS" stands for "Infanterie Spitsgeschoss" which means "sharp bullet, infantry"
When you pick up an early Mauser, look for the letter "S" to be stamped on the receiver somewhere. Be real careful with those early Mausers because if you fire a .323" bullet down a .318" bore, you will have a bad day.
The 8mm Mauser is sometimes referred to as the 8x57mm JS. The "J" part is an error. The problem started back after the end of WW1. An American miliitary translator was looking at the German blueprints for the round, and he misread an ornate gothic "I" as being a "J". And this misnomer has persisted ever since.
And if you have a .318" Mauser, not to worry. You can get bullets in this diameter from Dave Cumberland over at Old Western Scrounger.
And if you want a perfect load for the 7.92x57IS, here it is:
200 grain Speer bullet, and 44 grains of IMR-4064. The muzzle velocity is 2400 fps, with a standard deviation of 20 fps. And it is soft shooting too.