If I am not mistaken, the Managing Authority is that component of the CF that is responsible for the affairs of an entire MOC(or "trade"). For example, the MA for the 031 MOC (Regular Inf) is the Army. The MA for Boatswain is the Navy, etc. Some MOCs, mostly in the technical branches, are not quite so simple. So, the MA is more concerned with the collective issues of the MOC as a whole, such as its training, servce affiliation, etc. The Army has recently tried to become the MA for some of its support MOCs, but with limited success.
The Career Manager is an individual Officer or WO who is employed in NDHQ to focus on the military employment of individual members of MOCs. The CM does not make decisions (contrary to popular misconception.....) he is in fact a servant of the wishes of the particular Corps, Branch or Regiment. Those agencies make the important decisions, and the CMs put things into effect and manage the system. In the Infanty, for example, COs and RSMs of battalions have traditionally had great influence on career issues and are still really the CMs for officers below Capt and NCM below Sgt. So, the CM is more concerned with individuals within an MOC.
Hope that helps. Cheers.