I'm not expert. Let's get this out of the way first.
However I've read, been told, and had confirmed from a Rock River Arms distributor that the .223 version is a civilian version round and the 5.56 version is the military version and the only difference is the 5.56 version (nato) runs at higher case pressures which is of no consequence if you have a barrel rated for NATO/5.56 round.
But if you have a .223 rated barrel and run 5.56 rounds through it,... well I can't say for sure your rifle will explode but overpressures aren't exactly optimum conditions and would tend to void any warranty.
You other fellas can correct me if I've been misinformed.
Me either. Not by a long shot (pardon the pun). Your understanding of the situation sounds perfectly good to me.
I was addressing only the "size" issue FreeNot raised, and not case pressure. In particular, I was talking only about bullet and bore diameters.
My understanding (and as I've learned so many times here on FreeRepublic, that's often seriously flawed!) is that "caliber" is measured in inches, whereas the other commonly encountered designation is a metric one. So .223 cal = 0.223 in = 5.66 mm > 5.56 mm. Bullets expand in the bore and make contact with the rifling, so you can fire a slightly smaller bullet through a weapon having a slightly larger bore diameter than the bullet (I've often heard people talking about firing a .44cal round through a .45, say, though I don't think I'd like to try it). So I've always thought of .223 and 5.56mm being approximately the same round, at least as regards their diameters, certainly not their muzzle velocities.
Okay, now if I've weaseled enough on that one, I won't be flamed too badly! :-)
Now that's not a problem for most folks except for those that purchase South African or Israeli Military ammo........or the Operators with lots of free goobermint ammo........gosh I miss the good old days .
Stay Safe !