Pressures on both work out to be the same. 60,191psi (CIP) for the 7.62 NATO vs 60,191psi (CIP)/ 62,000 PSI (SAAMI) for the .308. Same pressure, different measurement methodology.
CIP requires all the chamberings to be proof-tested to 125% of their rated capacity - hence the CIP standard proof figure is 75,275psi.
Compatibility comes from the very slight differences between the NATO and .308 spec chambers.