There are a lot of myths about military brass, and things have also changed a bit over the years.
Let's talk about 7.62 NATO and .308 Win first as the situation was fairly straight forward until fairly recently (around 2009).
In the past you could rely on 7.62 NATO brass being thicker walled and significantly lower volume than .308 Win brass. That was done intentionally to give the case a thicker web to prevent head separations in machine guns like the M60, where the head space was usually very generous.
Generally speaking, after the M14 dropped out of common use, handloaders avoided non match 7.62 NATO brass as most of it was loaded as M80 ball or M62 tracer rounds, and fired in an M60, with the result that the cases were almost always stretched excessively.
Match brass ammo however was highly sought after as the quality was usually good and the cases were not abused. They also didn't have a crimped in primer and were easy to process. They still however had the thicker web and smaller internal volume as it was the same brass, just more carefully selected by lot, then head stamped as match brass and assembled without a primer crimp.
The difference in powder charge to achieve the same velocity was normally in the 1.0 to 1.5 grain range - fairly significant if you were loading a fairly warm load for .308 and dropped it in a 7.62 NATO case by mistake. Since I had 5 gallon bucket fulls of LC Match brass, I loaded everything into it and never bothered to develop loads for .308 commercial cases and if by chance a .308 case found its way into a batch the result was lower than normal pressure.
However that has now changed.
When Federal started producing the latest iteration of M118LR as well as Mk 316 Mod 0 for the Navy, they started using their Federal Gold Medal Match brass, which was head stamped as Lake City Match brass, as Lake City is operated by Federal. That change meant this newer LC Match brass has the same volume as commercial .308 brass and in particular commercial FGGM brass, which is what it is. I found this out when I started to run low on military match brass, and had access to significant amounts of once fired FGGM .308 brass from accuracy testing by HS Precision on our club range.
I started developing loads in FGGM brass and then bought some newer production Lake City Match brass and discovered I was using the same load in each. A little research uncovered the switch to FGGM brass when Federal got the M118LR contract.
To make things even more confusing, you can also find Federal packaged Lake City brass sold as a reloading components stamped as regular non match military head stampeded Lake City brass. It's the same brass they use in their civilian XM-80 load, and again it has the same internal volume as commercial .308 brass. So can't rely on military marked non match brass all being thick walled either.
In short, the former truth that 7.62 NATO brass was thicker and lower volume than commercial .308 brass is no longer always the case.
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5.56 NATO and .223 Rem
This is much more straight forward. The case was designed from the start for the AR-15, as an upsized .222 Rem, and Stoner stated once that had be known Remington was developing the .222 Remington Magnum, he would not have bothered with the .223.
Any bottle necked case stretches at the point just behind the spot where the case still adheres to the chamber. Under pressure the case expands to seal against the chamber and it does so all the way back to the point where the case wall is too thick to expand. That depends on the pressure of the case, the thickness of the case wall, and the diameter of the case as the smaller the diameter the more resistant it is to pressure.
If you've ever had incipient head separations with 7.62 NATO and 5.56 NATO brass you've probably noted the separation line develops fairly low in the 7.62 NATO case maybe 1/4" to 3/8" above the extractor cut. In contrast, it's about 40% of the way up the side of the case in the 5.56 NATO.
That's why you see a great deal of difference between 7.62 NATO and .308 brass. There's a lot of case in front of that separation line in the 7.62 NATO and .308 Win, and that makes it much more likely for a case to separate and leave part of the case in the chamber. That's why 7.62 NATO brass ended up with thicker case walls than .308 Win.
However, you'll find no significant difference in the case wall thickness and internal volume of most military 5.56 NATO brass and civilian .223 Rem brass. There's no need to construct it differently to avoid a separation that leaves the front portion of the case in the chamber.
Someone above suggested that 5.56 NATO ammo made to be used in belt fed weapons is different and has thicker case walls. I'll be really charitable and say that I'm dubious. That is no different than putting an entirely new round in the logistics system, and not just in the warehouse and transportation system but all the way back to the manufacture of components, meaning to separate types of 5.56 NATO cases would have to be made and kept separate through the manufacturing process.
That's just not going to happen. If it was felt case walls needed to be thicker for the SAW, they'd just use a thicker case on all 5.56 NATO ammo.
In short, all domestically produced .223 Rem or 5.56mm NATO ammo has very similar case capacity and for all practical purposes the cases are interchangeable.
The potential exception are 5.56/.223 cases manufactured in some eastern european countries. Some of them are *reported* to be lower capacity, but I've never personally come across a valid example.