The law of April 16, 1862, didn't require a discharge if one was under or over age -- otherwise substitutes over or under the age limits couldn't have been accepted. By the same token, unless a man enrolled as a substitute, he couldn't be compelled to serve if the law didn't oblige him to be enrolled. On this basis soldiers frequently sought and received discharges. Sometimes parents of boys under the age of eighteen wrote directly to the Secretary of War to obtain discharges from the army.
Those who didn't seek discharges continued in service as volunteers, AKA exempts.