The .308 Winchester is the commercial version of the military 7.62X51mm NATO.
The .308 Winchester and the 7.62X51mm are not identical and there are minor differences in the inner case dimensions, though SAMMI (Sporting Arms and Ammunition Manufactures Institute) does not list either cartridge in a firearm designed with the other as unsafe.
.308 Winchester and 7.62X51mm NATO do interchange and either are safe to use for your rifle.
Good to go in that rifle. For practical purposes they are the same. If the rifle is chambered for the .308, it will handle the pressures of the NATO round.
HK's and CETME's with the fluted chambers are another story. You are OK
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