Numbers 1 and 2 are not correct. 5.56mm NATO and .223 Remington are identical in external dimensions. If you measured both cases you would not be able to tell the difference without a headstamp.

#3 is partially correct. Mil-Spec brass can be heavier (i.e. have thicker case walls) than some .223 ammo, though some ammo manufacturers load SAAMI 223 Rem loads in mil-spec brass. This is because Mil-Spec 5.56mm ammo is loaded to 60,000 cup vs. the SAAMI .223 Rem max operating pressure of 50,000 cup. It's also because the 5.56 ammo has to be able to take one heck of a beating without being deformed in order to reliably function through automatic weapons under combat conditions. Machineguns and machinegunners beat the snot out of their ammo, and the thicker cases also help reduce cook-offs as well.

Now, aside from the added pressure that 5.56 NATO ammo is loaded to, there is also a difference in the CHAMBER of a 5.56mm rifle versus a .223 Remington chamber. The 5.56 NATO chamber has a much longer and generously cut freebore and a shallower angle as the bullet engages the rifling. This mitigates the higher pressures generated by the 5.56 loads at the potential cost of some accuracy. The SAAMI compliant .223 Rem chamber uses a much shorter throat with a steeper angle between the freebore and rifling. This improves accuracy, but also significantly increases peak chamber pressure. SAAMI spec 223 Rem ammo is loaded to lower pressures to accommodate the shorter freebore without creating a dangerous condition. But when you shoot mil-spec 5.56 NATO ball ammo in a .223 chamber, not only is the round loaded to 10,000 cup more pressure, but combine that with the much shorter freebore and pressure can further spike as much as 20,000 cup higher, or 80,000 cup, which is EXTREMELY high and potentially very dangerous. The good news is that most modern rifles are tough enough to handle such pressure, at least for awhile, without failure. But if a case ruptured, or metal fatigue sets in from repeated overpressure, you could wind up with a face full of shrapnel with no clear sign of impending failure.

The moral of the story is that you should NEVER fire and cartridge stamped 5.56 NATO in a barrel stamped .223 Rem, unless you've contacted the manufacturer to make sure the throat is cut to 5.56 specs. I understand that the Mini-14 is an example of such a case, where Ruger stamped the barrels .223 Rem but it's got a mil-spec chamber because they figured that some people would ignore the barrel stamp and fire 5.56 ammo through them. Some AR's also are (incorrectly) stamped .223 Rem when they are 5.56 chambers. Only the manufacturer or a gunsmith with a chamber mould can confirm the actual chamber specs. When is doubt, don't shoot 5.56 ammo in a .223 Rem chamber.

All that said, the reverse is not true. If you have a confirmed 5.56 NATO chamber, it is perfectly safe to shoot .223 Remington ammo in it. The only negative consequence may be slightly reduced accuracy and velocity, but it is completely safe.

Many AR manufacturers are now chambering their rifles in 5.56 NATO Match, or .223 Wylde. These chambers are both compromises between the 5.56 NATO and .223 Rem chamber, in order to allow the safe use of mil-spec ammo, while not sacrificing as much accuracy.

Mike