8x56 MS often can be made by shortening 8x57 Mauser or even .30-06.
The base IS smaller, but only by a theoretical .005". Chamber tolerances and brass tolerances can make this up with just a bit of luck.
Base of 8x57 = .470"
Base of 8x56MS = .465"
8x56MS is emphatically NOT the same as 8x56R which was issued for the Mannlicher straight-pulls in the 1930s.