A properly drafted man with no prior military service was taken into the United States Army as a Private. and sent one of many Basic Training Camps i.e. Fort Dix, New Jersey where he was to complete 8 weeks of Basic Military Training before being given an MOS for which he would receive additional training at the same or another Military Base. A drafted man during Viernan was expected to complete 2 years of active service from the time he took his oath. He was never considered an enlisted man as enlisted men signed up for service and usually for a specific field of duty and depending on that field of duty, they were expected to spend at least 3 years of active service in the army.
Once you're in the military, you are either "enlisted" or "officer" for pay purposes. Almost all draftees become enlisted, but a few professionals (primarily doctors and lawyers) may be drafted and sent to Officer Candidate School instead of Recruit Training Camp.