There are two issues here: chamber design and ammmo specifications.

The 5.56 chamber is, ah, generous in certain areas to ensure function in full auto weapons under sustained fire conditions. To the point that some chambers which will pass a 5.56 mm chamber gauge will fail a .223 no-go gauge.

The ammo spec difference is due to the 5.56 mm having a velocity requirement for a 20 inch barrel at 78 feet which is higher than that generally produced by .223 with comparable bullets/barrel length. This requires a higher than SAAMI specification pressure.