The cartridges are the same dimensions. 5.56 CAN be loaded to slightly higher pressures. That doesn't mean it is always loaded to the red line. In fact, virtually all 5.56 factory loads will still be loaded to pressures within 223 specs. If you're a hand loader and push the envelope with your loads, you can get a little more pressure with 5.56.
Semi auto, and full auto rifles stamped as 5.56 have slightly different specs for the chambers than 223. This is primarily to improve reliability. Either cartridge will chamber and fire in either chamber. If you have a rifle stamped 5.56, they are completely interchangeable with 223.
If you have a semi-auto stamped 223 and fire 5.56 ammo through it you MIGHT run into reliability issues, and repeated use MIGHT result in premature parts breakage. But there are currently no semi-auto rifles being made with 223 chambers. The only one ever made was the very early Ruger Mini-14's and those have been stamped 223/5.56 for at least 30 years. In a bolt rifle you'll never have an issue.
At the end of the day, yes there are very, very minor differences in allowable pressures. And 5.56 chambers are usually cut on the loose side to enhance reliability; 223 chambers are usually cut to tighter tolerances to give better accuracy.
Some perspective.
The 30-06 was put into service in 1903 with modifications in 1906. Since 1903, 30-06 loads have been upgraded 3 times with modern factory loads capable of 400 fps more speed than the original loads. There are 4 different power levels available for 30-06, with a far greater range of pressures and velocity than 223/5.56. And not all of them are compatible with all 30-06 stamped rifles. Yet, we don't have 4 different designations for 30-06.
The chamber dimensions on 30-06 rifles over the last 120 years and between dozens of manufacturers have varied considerably as well due to manufacturing tolerances. If you have 30-06 rifle, you're far more likely to run into an ammo incompatibility issue than shooting 5.56 in a 223 chamber.
