While there are some differences between the 308 WCF and the 7.62x51 Nato, since around 1976 I have been shooting both in rifles "labeled for one or the other" with no problems.
By that, I mean, I have interchanged 308 ammo and 7,62x51 ammo, and 308 rifles and 7.62x51 rifles, in every possible combination, from several different countries, including some military 7.62 ammo from non NATO countries with NO problems.
And I am talking several different rifles, and THOUSANDS of rounds fired.
308/7.62x51 NATO, I have never seen any PRACTICAL/FIELD differences...