19glendale,
Yes, they are the same. The original military 8x57 cartridge was the 8x57 Infantry(hence 8x57I)when they made it with a rim for drillings,etc;this cartridge was the 8x57Infantry Rimmed (8x57IR).In old German script, an I looked like an English J ,to some people,so it was usually written as 8x57JR in English.The "S" in 8x57IS and 8x57IRS stands for spitzer.When they reduced the weight and increased the velocity, they increased the rifling depth and bullet diameter(to .323")so the bullets would "hold the rifling".
This bullet was a spitzer.The 7.8 57 is not really the cartridge designation, rather it is the bore diameter(not groove or bullet dia.)as measured by the proofhouse with "plug guages" and the legnth of the case.The nominal cartridge designation is 8x57IR.Note that I have a drilling also marked 7.8 57, that is chambered for an entirely different cartridge-8x57R/360.Don't feel bad if you are confused, most people are, even those of us that think we understand it.
Mike