Commissary duties involved food for the troops.
Quartermaster duties involved all other items supplied to the troops except arms and medicial services. This includes military equipment, uniforms, transportation, tents, housing, official forms blank paper, pens and ink, pay and flags, to name some of the standard items.
It's quite unusual to find officers whose duties encompassed both the commissary and quartermaster departments. Filling out the necessary requisitions, receipts and reports would have overwhelmed most good accountants.
Also, since arms were generally in short supply, front line troops were issued the best weapons. Men assigned to either the commissary or quartermaster departments got cast-off weapons or none at all, usually the latter.