OIC is also, in the TLA-filled jargon of the United States' military, the Officer In Charge--which is just like it sounds, the commissioned officer in charge of some particular building or directorate or suchlike. The difference between the OIC and the NCOIC--aside from the fact that the NCOIC is a non-commissioned officer--can be expressed as follows. When I was at Ft Leonard Wood, MO, doing Basic Training, there was a "Consolidated Troop Medical Clinic" where we went on sick call. The NCOIC there was a Sergeant First Class (E7) who was--first and foremost--a soldier, although he had been trained by the Army Medical Corps, and it was his duty to take charge of the troops and trainees who came in, and to directly supervise the enlisted personnel who handed out things like Tylenol, Sudafed, specially padded sole inserts, etc.--all the things that could be easily given to those suffering from common and minor aches and pains.
The OIC, on the other hand, was a Captain. He had gained his commission, not from being a soldier and working his way up, but rather by already being a doctor and then joining the Medical Corps, where he'd undergone basic soldierization training. In his charge were the general direction of the clinic (subject to his own supervisors, of course). He saw those patients whom the enlisted personnel couldn't deal with, made diagnoses, wrote prescriptions, and supervised the NCOIC. He was, in a sense, the CEO of the clinic, with the NCOIC as his management.
OIC as an acronym is not anywhere near as prevalent as NCOIC, at least in the Army, where the large majority of troops are enlisted.