You kind of have your acronymns mixed up.
C.O. : Is short for Commanding Officer, or the guy in charge. For instance, you can be a Captain, which is an officer, but he is not in a command position, such as a staff intelligence officer, or personnel officer. A "CO" is usually a job description. A captain, lieutenant, Major, or Lieutenant Colonel can hold a command position, but they usually rotate in and out of command positions depending on their field or specialty.
A commisioned officer is one who gains his rank by going to OCS (Officer Candidate School) such as myself, or ROTC (Reserve Officer Training Corps) or a direct commision for people that have particular training or skills such as lawyers, doctors, dentists, ministers, rabbis, or priests.
A non-commissioned officer are Corporals or above (sergeants, etc.). They do hold supervisor positions, but do not "command". The NCO's are the backbone of the Army.
Generally speaking, Commissioned Officers make policy or give direction for whatever task needs to be done, and the NCO's execute the plan or complete the mission.