Ok, here it is...
7.62 NATO Ball (147-150 gr) is loaded to lower pressures. than .308. You can shoot any 7.62 NATO Cartridge in any .308 (see above for an exception...). If you have an older Battle Rifle like an M-14/M-305/M1A it's a very bad idea to shoot .308 Win with Projectiles heavier than 178 gr. Also burn rate is an issue with M-14 type rifles.
All this confusion comes from 5.56 NATO vs. .223 Rem. The only real difference between these two is chamber dim., esp. the throat, it's longer (5.56). If you are shooting 62 gr Ball in an older .223, or one throated for light bullets you could have pressure issues...but since it won't stabilize in a 1 in 12 (or 1 in 9 for that matter) why shoot it.
So, as a loose rule no .308 in the 7.62, and no 5.56 in the .223. If it's a recently made .223 with a 1 in 9 twist, or something like an AR-10/102 they are interchangeable.