David, I haven't done much research on Union troops, but as regards Confederate troops, Catton is correct (I can't believe how arrogant that sounds--a guy like me vetting Catton!)

Confederate "returns of troops" normally reported the number of men present for duty, absent (furlough, hospital, absent without leave, detailed on other duties, etc.) and "present and absent" or "aggregate". The numerical differences between "present for duty" and "aggregate" were typically huge. The Confederate army did not have a large supporting arms organization. Most of the cooks, clerks, teamsters, nurses, provost guards, etc., etc., were men detailed from the line regiments. I have read correspondence from some Arkansas regiments, wherein company and regimental commanders complained that up to a quarter of their men were detailed to other, non-combat duties. It was a real problem for the army, and something that modern students of the war need to take into account when analyzing force numbers.