223 brass is generally primed with a standard Boxer Small Rifle primer. There's a slight difference between the 223 and 5.56mm cartridges, but the brass looks quite similar when you're sorting through it, hence they're both going into one article.
If you're dealing with a mixed load of brass, you may have Berdan-primed cases mixed in. I would not recommend trying to process Berdan brass in 223. In most shooters' case, it will only be encountered frequently enough to be a mild irritation, and not as a significant source of reloading brass.
Known Berdan-primed 223 Headstamps
"86 13", where 86 is printed above the primer and "13" is printed on the bottom.
An alert reader pointed out that there's a lot of crimped 5.56mm brass out there. Crimped primer pockets are too tight to fit a primer into, and it's necessary to swage them (expand the pocket out to spec) before you can insert a primer into the brass. If you try to insert a primer into a crimped pocket, you may end up detonating the primer. Usually, but not always, crimped brass has a crosshair printed on the headstamp (+ within a circle). However, the presence of a crosshair doesn't guarantee that the brass is crimped - only that it was crimped at some point. If you're using brass someone else has reloaded before, they'll have swaged the primer pocket out.
-- SeanNewton - 30 Mar 2007