No it's not the same brass (if your comparing 223 brass to 5.56 NATO brass) NATO 5.56 brass has a higher SAMMI pressure rating (62,336 psi) and the casing wall thickness runs about .012" and has less internal case volume capacity . Standard .223 casings , thinner wall thickness at about .010" , greater case capacity , lesser pressure rating (55,000 psi). Lastly 5.56 casings have a slightly smaller neck OD than 223 casings by about .002".Then why separate 223/556? Same brass.
I also like using AR specific "small base" dies to ensure consistent semi-auto feeding . Small base dies size right to the minimum casing dimensions.