Which is proper chief of staff or Chief of Staff?
Chief of Staff is a proper title.
Yes, the Chief of Naval Operations (CNO) is a service chief. The CNO is one of the "Chiefs" that make up the Joint Chiefs of Staff. The others are Chief of staff of the Army, Commandant of the Marine Core, Chief of Staff of the Air Force, Chief of the National Guard Bureau, and the Chairman & Vice Chairman of the Joint Chiefs of Staff.
Admiral Mike Mullen is Chief of Staff for the U.S. Navy, and is the current Chairman of the Joint Chiefs of Staff. General James E. Cartwright is Chief of Staff for the U.S. Marine Corps, and is the Vice Chairman of the JCS. General Martin E. Dempsey is the Chief of Staff of the U.S. Army. He is currently the nominee (pending Senate confirmation) to replace retiring Admiral Mike Mullen as the next Chairman of…