A DM or Dive Master is a professional rating that entails months of training and work. In the end a DM must carry liability insurance and is often tasked with supervising student divers on a course, or certified divers on excursions or trips.
A Master Scuba Diver is a recreational level rating, which is obtained when a diver has completed 5 specialty courses and has a minimum number of dives. The Master Scuba Diver cannot supervise or act in a supervisory capacity of other divers at any time, as they do not have the requisite training, experience or insurance.
The definition may vary somewhat from one agency to another, however the basic premises is the same as with the PADI standards, where only a DM, Assistant Instructor, Instructor, or higher level of professional level of certification, can supervise other divers or students and receive monetary compensation for this service.
Hope this answers your question.