All of the above is correct. But one other factor distinguishes .223 from 5.56mm ammunition - peak chamber pressure. SAAMI pressure specs govern .223, while NATO pressure specs govern 5.56mm. These are two completely different measurement methods and are not related. However, I have read that if 5.56mm military ammunition is pressure tested using the SAAMI method, the peak chamber pressure of 5.56mm somewhat exceeds .223, i.e., the 5.56mm NATO rounds are loaded somewhat "hotter" than civilian .223, but both are within their respective pressure specifications.
The only difference between the American SAAMI .223 and Military 5.56 is the length of the throat. All that NATO standards means is Europe get to keep using their CIP standards of measuring chamber pressure at the mouth of the case. Our American SAAMI measures chamber pressure at the mid point of the cartridge case. American SAAMI .223/5.56 read as 55,000 psi and European CIP (NATO) pressures would read as 62,000 psi at the case mouth.
Below are the military milspec pressure requirements for the 5.56 that are used by commercial ammunition manufactures making 5.56 ammunition for our military. Please note that our military even when using the copper crusher method uses the term PSI. This sometimes causes confusion when people look at TM 43-0001-27.
The pressure standards below are the same as for the American SAAMI .223.
MIL-C-9963F
15 October 1976
MILITARY SPECIFICATION
CARTRIDGE, 5.56MM, BALL, M193
3.7 Chamber pressure.
3.7.1
Measurement by copper-crush cylinder.-The average chamber pressure of the sample cartridges, conditioned at 70° ± 2°F, shall not exceed
52,000 pounds per square inch (PSI). The average chamber pressure plus three standard deviations of chamber pressure shall not exceed 58,000 PSI.
3.7.2
Measurement by piezoelectric transducer.-The average chamber
pressure of the sample cartridges, conditioned at 70° ± 2°F, shall not
exceed
55,000 PSI. The average chamber pressure plus three standard
deviations of chamber pressure shall not exceed 61,000 PSI.
Traditionally military chambers are larger in diameter and have longer headspace settings. Look at item C below, the military chamber is .002 larger in diameter. The military throat is larger in diameter and longer than SAAMI "recommendations" see items G and N
The throat on my Savage .223 with a 1 in 9 twist is .0566 and "LONGER" than military requirments. .223 rifles with a 1 in 12 or 1 in 14 twist normally have the shorter "SAAMI" throat and if 5.56 M855 ammunition is fired in them the pressures will be 5,000 psi higher than normal "rated" .223 ammunition.
Again the SAAMI interchangeability warning for the .223 and 5.56 did not come out until 1979 with the adoption of military M885 ammunition and the change in military throat length.