The .308 Winchester and the 7.62 NATO cartridges are similar in size, but slightly different in chambering, thickness of the cartridge case, and pressures in loading. The 7.62 NATO cartridge may be safely fired in a .308 Winchester firearm. The reverse is not always true.
NATO standard refers to the standard round used by all NATO countries troops so if a country is operating with another country and the guy from the other country runs out of ammo he can pick up the other mans ammo. The NATO standard for Assault Rifles is 5.56X45mm NATO and for pistols 9X19mm NATO.
NATO as it exists today has over ever been called NATO. However, a precursor to NATO, which did not include the USA, was the Western Union Defence Organisation, a defence council set up by the UK, France, Belgium, Luxembourg and the Netherlands.