Yes....and ...no!
A .300 Win Short Mag and .300 Rem Short Action Ultra Mag, .300 Ruger Compact Magnums (and the short Lazzeroni offering, what ever its called) are .308" calibre magnums, that are shorter than the common magnums that came before them.
The .308 Winchester is a different cartridge altogether. It too is considered 'short' but is not nearly as wide in the case as the much newer 'short magnums'. The .30-30 is also a .308" calibre cartridge but has less case capacity than the .308 Winchester.
The other big factor is the chamber pressure that these cartrides are designed for. I don't have the numbers with me but the .308 Winchester, like most of the common non-magnum calibers operates at a maximum of about 60 000 - 62 000 psi chamber pressure, the short magnums at a max of 65 000 and the old .30-30 much lower than that, little over 40 000?)
.308 refers to the bore diameter between the grooves of the rifling, .300 between the rifling lands.
Cartridge nomenclature can be confusing but almost all the '.30' calibres use a .308 bullet (except the .303 Brit, 7.7 Jap, 7.62x39 and 7.62x54R -well some rifles chambered for the latter 2 do in fact use a .308, not the .311"/7.7mm!).
This means the .30-30, .308, .30-06, .300Win, .300 WSM, .300H&H, .300 SAUM, .300Ultra, .300 Weatherby, .300 Blaser, .30R Blaser etc etc etc all use the same diameter bullet - .308". Each one has a different case capacity and there are different maximum operating pressure specifications that rifle and ammo makers adhere to. Most cartridges fall into only a few different max pressure spec bands. Therefor a .308 Win way outruns .30-30 because 1) it holds more powder and 2) it operates at a much higher chamber pressure, therefore pushing the bullet with more force.
Thats the summary description
