The deal with the .308/7.62x51 is opposite of the 5.56/.223.
If you have a rifle chambered in commercial .308, you can shoot 7.62 surplus in it all day. The .308 commercial loads are generally higher pressure than the 7.62, so a commercial rifle can take it. It is not recommendable to shoot hot commercial .308 loads in a military rifle chambered in 7.62. As far as chamber dimensions, I think they're identical.