.308 ammunition and 7.62x51 ammo are dimensionally the same. 7.62X51 may be loaded weaker or hotter than .308 commercial ammo, it depends on the load and the manufacturer.
Military arms are designed for military loads of a certain specification, so a firearm like a Cetme or an FAL may shoot some commercial ammo well, and it may have problems with heavier commercial hunting loads and heavier bullet weights (mil spec ball is usually loaded with 147-150 grain bullets).
A military spec 7.62x51 chamber can suffer more errosion and meet spec, or could be a little larger than a .308 saami chamber.
I have a saiga .308 it fires milspec ammo just fine, and it also fire commercial ammo just fine. the .308 spec means that it meets saami spec for .308, so it May Be little tighter than a military 7.62x51 chamber, depending on the military arm you are comparing it too.