In the days when the USA had conscription, once someone was drafted, he was sent an official document called "Order to Report for Induction". I'm sure many of those who reported as ordered, and were inducted into the military were somewhat less than "volunteers." According to the dictionaries I have checked, "to draft" someone is to select them from a larger group for a specific purpose - in this case military, but the verb is also used to refer to selections for professional sports teams. "To induct" is to bring the draftee into the military service.
Originally, I had written "To induct someone is to enlist a person, who is often a volunteer." I should have left it. I agree that the induction process is simply admitting both volunteers and draftees. Drafting someone remains conscription for me.
To me it's not just a matter of choice or compulsion. If you're drafted, you're drafted when the lottery machine spits out the ball with your number on it (or however it's done), or when you receive the letter through your letter-box telling you that you've been chosen. You are inducted when you arrive at the army camp and are issued with a uniform, and told where to sleep, where to eat, and so on. The process of introduction is the induction.