Long story short, there's a lot of NATO and Soviet rounds that sound similar in nomenclature. But being designed independently by competing nations, they're dramatically different.
7.62x39 was designed as an assault rifle cartridge, not a full rifle cartridge. .308 (7.62x51) was designed as a full rifle cartridge. .308 is fairly close to 7.62x54R in construction, but there's still some major differences, not the least of which that 7.62x54R is a rimmed cartridge whereas .308 is rimless, and 7.62x54R is a heck of a lot hotter than .308.