OK you are right there are two different 8 x 57 mauser cartridges (actually there are three). I think you are getting confused by the shoulder angle, both figures are technically correct, ignore the should angle. The two cartridges are the 8 x 57J and the 8 x 57JS, the latter has a larger bullet diameter(.323) and produces a higher chamber pressure than the former. The 8 x 57JS was introduced in 1905 and all German 98 military rifle should be chambered for cartridge. Model 1888 rifles and some later sporting rifle will be chambered 8 x 57J. You should not fire a full load 8 x 57JS cartridge in a 8 x 57J chamber (you may blow the gun up). Due to confusion, 8mm Mauser sporting ammunition sold in North America is loaded to produce a safe moderate pressure, so it is safe in either chamber. This is not the case with European 8 x 57JS, it full pressure (50,000 psi).
So to answer your question, first determine what you have, if in dout ask a gunsmith. Second, always check the headspace on old guns with the correct no-go guage (available from Brownells). Again it may be cheaper and easier to get a gunsmith to do the checks.