7.62x51 or 7.62 NATO and the .308 Winchester are sometimes
identified as being the same cartridge.
There are some differences in ammo and it is risky to generalize.
7.62 Nato military brass can be harder; .308 Win brass can be softer.
Most 7.62 NATO caliber rifles will shot both.
Most .308 Win rifles will shot both.
Some 7.62 rifles will not feed some .308 Win softnose ammo.
Some 7.62 rifles have problems with soft civilian brass.
Military bullets, powders and primers may be hard on a fine
target bore, or may simply require frequent thorough cleaning.
This is from a few hundred rounds experience with a
Savage 110 in .308 Win, and FAL and CETME in 7.62 NATO.
Test samples of ammo, buy lots of what works best in your gun.