7.62 vs .308
From wikipedia:
"NATO 7.62x51mm cartridge is nearly identical to the commercial .308 Winchester. NATO controls specifications for the military round while SAAMI controls specifications for the civilian round. The organizations have established two differences: the standard pressure is 50,000 psi, as measured by the copper crusher gauge, for most military rounds, while the SAAMI maximum is 62,000 psi, measured with a piezoelectric gauge, for the civilian round. Since the two types of gauges give different pressure readings, the two pressures cannot be accurately compared. The NATO M60 High Pressure Test round is loaded to a pressure of 67,500 psi, so military arms should be capable of handling the pressure of civilian rounds. The military chamber is specified to be 1.645 inches, compared to the civilian chamber of 1.632 inches. Though this difference is just 0.013 inches, a chamber of acceptable military length will put excessive stress on the thinner civilian brass, causing premature head separation. While it is safe to mix .308 and 7.62x51mm ammunition, problems will not be encountered if the correct caliber designation is used."
So .308 is certainly okay in a mil spec gun, but not necessarily the other way around.