Look on the lower and barrel and see if it is rated for. 223 only or 5.56. Shooting the former in the latter can cause problems. (The reverse is fine though.)
You have it exactly reversed.
5.56 has higher pressure than .223.
You can safely fire .223 in 5.56, but not the opposite.
That being said, lots of people do it anyway.
.223 Wylde will fire both. The throat length is a compromise between the two.
• The cartridge shellcases of each have essentially the same length and exterior dimensions. • Mil Spec 5.56mm ammo typically has higher velocities and chamber pressures than the .223 Rem. In fact, the chamber pressure of each is tested by entirely different methods in different chamber configurations. The resulting data cannot be meaningfully interchanged or interpreted by applying a simple correction factor. • The 5.56mm cartridge shellcase may have a thicker sidewall and a thicker head than the commercial counterpart - to better withstand the stresses generated by the higher chamber pressures. This situation, however, reduces the powder capacity of the military shellcases - which can create higher than safe pressures if reloaded using load data and components intended for commercial .223 Rem cartridges. . • The 5.56mm and 223 Rem chambers are also similar but are not identical. The primary difference is in the "Throat”. The throat is defined as the cylindrical portion of a chamber between the shellcase mouth shoulder and the conical “Leade” portion that tapers down to the bore dimension. The throat in a. 223 Rem chamber usually extends only .085” in front of the shellcase mouth position. In a 5.56mm chamber the throat is typically .162”, or almost twice as long as in the 223 Rem chamber. • One can safely fire commercial 223 Rem. cartridges in military 5.56mm chambers with this longer throat, but will usually experience a slight loss in accuracy and velocity – compared to firing the 223 round in the chamber with the shorter throat for which it was designed. • Functional and safety problems may occur when firing the higher pressure 5.56mm cartridge in a 223 Rem chamber with its much shorter throat. It is generally known that shortening the throat can dramatically increase chamber pressure. In some instances, this higher pressure can result in primer pocket gas leaks, blown cartridge case heads, and poor gun functioning, each of which can be personal safety issues. • The 5.56mm military cartridge fired in a 223 Rem. chamber is considered by SAAMI (Sporting Arms and Ammunition Manufacturers Institute) to be an unsafe ammunition combination and is listed in the “Unsafe Arms and Ammunition Combinations” Section of the SAAMI Technical Correspondent’s Handbook. It clearly states; “In firearms chambered for 223 Rem – do not use 5.56 Military cartridges.” • Federal’s XM193 packaging currently has a warning that states “For use in standard 5.56 Chambers. Do not use in non-standard 5.56 chambers.” This warning is also listed on the XM193 Product Specification Sheet. Winchester Ammunition has a similar warning on their USA brand 5.56 ammunition packaging: “Use only in firearms in good condition designed and chambered by firearm manufacturer specifically for this 5.56 ammunition and so marked on the firearm.” • Some commercially available AR15’s, M4’s and M16’s – may in actuality have been manufactured with 5.56 mm chambers although stamped .223 Rem on the receiver. it is the user's responsibility to know for which cartridge their firearm was chambered and choose their ammo accordingly. If you have any questions about chambering, check directly with the firearm manufacturer.