From my time in the military and a lot of range/hunting time. Not to mention being an armorer for my dept. at one time. Here are some of the differences that I know of between the two.
The 7.62x39 is an intermediate round that is good to about 300 meters. Usually shoots a 123-125 grain bullet. Was first designed to be shot out of the SKS as far as I know and then the AK-47 came along. Also the Russian round tends to have dia. of .310 to .311
The 7.62x51 NATO is full size battle rifle round that works good in full auto machine guns not to mention semi auto and the famous 308 bolt actions. I don't want to get into the interchangeability of the two but they are very close. The NATO round is usually found in 150 grain bullets and heavier and is good to around about 800 meters. The NATO round has a dia. of .308
While there are some out there with a lot more knowledge than myself I am sure some will disagree with me. This should be enough to show you the differences though.
