This is an excerpt from a very detailed composition on AR15.com some time ago. I don't have the link but I saved the document:
Q. What is the difference between 5.56×45mm and .223 Remington ammo?
In the 1950's, the US military adopted the metric system of measurement and uses metric measurements to describe ammo. However, the US commercial ammo market typically used the English "caliber" measurements when describing ammo. "Caliber" is a shorthand way of saying "hundredths (or thousandths) of an inch." For example, a fifty caliber projectile is approximately fifty one-hundredths (.50) of an inch and a 357 caliber projectile is approximately three-hundred and fifty-seven thousandths (.357) of an inch. Dimensionally, 5.56 and .223 ammo are identical, though military 5.56 ammo is typically loaded to higher pressures and velocities than commercial ammo and may, in guns with extremely tight "match" .223 chambers, be unsafe to fire.
The chambers for .223 and 5.56 weapons are not the same either. Though the AR15 design provides an extremely strong action, high pressure signs on the brass and primers, extraction failures and cycling problems may be seen when firing hot 5.56 ammo in .223-chambered rifles. Military M16s and AR15s from Colt, Bushmaster, FN, DPMS, and some others have the M16-spec chamber with a longer throat and should have no trouble firing hot 5.56 ammunition. The big difference between the two chambers is in the chamber dimensions. Military M16s have slightly more headspace and have a longer throat area, compared to the Error! Bookmark not defined. .223 chamber spec, which was originally designed for bolt-action rifles. Commercial SAAMI-specification .223 chambers have a much shorter throat, a smaller diameter bullet seat and less freebore than the military chamber. Shooting 5.56 mil-spec ammo in a SAAMI-specification chamber can increase pressure dramatically, up to an additional 15,000 psi or more.
The military chamber is often referred to as a "5.56 NATO" chamber, as that is what is usually stamped on military barrels. Some AR manufacturers use the tighter ".223" (i.e., SAAMI-spec and often labeled ".223" or ".223 Remington") chamber, which tends to give you more accuracy but, in self-loading rifles, less reliability, especially with hot-loaded military ammo. Some AR manufacturers use an in-between chamber spec, such as the Wylde chamber. Many mis-mark their barrels too, which further complicates things. You can generally tell what sort of chamber you are dealing with by the markings on the weapon, but always check with the manufacturer to be sure.
Typical Colt mil-spec-type markings: "C MP 5.56 NATO 1/7"
Typical Bushmaster markings: "B MP 5.56 NATO 1/9 HBAR"
Armalite doesn't always mark their barrels.
Opinion: In general it is a bad idea to attempt to fire 5.56 rounds (e.g., M193, M855) in .233 chambers, particularly with older rifles.
Fact: specifically warns against the use of 5.56mm ammo in .223 chambers. The .223 SAAMI specification was originally made with bolt rifles in mind
Q. Which should I be looking for in an AR15, 5.56 NATO or .223 Remington chambers?
This is really a matter of the role for which you plan to use your AR. .223 Remington chambers will give you slightly better accuracy, which is important for a match or varmint rifle. Any loss of feeding and cycling reliability and the restriction against shooting military ammo isn't as important as the accuracy gains for a rifle used in these roles, because for these rifles, accuracy is everything. People who just want to plink or who plan to shoot military ammo (such as most of the cheap surplus ammo available), and especially those who may use their AR as a weapon, should choose 5.56 chambers.
Opinion: Unless you have a reason to seek out .223 Remington SAAMI spec chambers, 5.56 NATO is probably the best solution. 5.56 NATO chambers still can have outstanding accuracy and give you more flexibility in ammo selection