The 5.56 chamber is the "looser" chamber, to allow for slight differences in NATO ammo, and to give slightly greater tolerances for increased reliability. The 223 rem chamber is a tighter chamber, which gives better accuracy with 223 rem ammo, but might or might not work well with all 5.56 ammo (223 ammo will function fine in 5.56 chambers).
The calibre marked on the lower receiver is does NOT tell you what the barrel chamber actually is, since lowers and uppers are easily changed (because of this, some new lower receivers do not indicate calibre). The upper reveiver, of course, has no calibre markings at all.
Only the calibre marked on the barrel tells you what the true chambre is. It could be mismarked, but I would guess that this is very rare. The only way to know for sure would be to use chamber guages.