Raph Koster has made a wonderfully concrete post about MUDs and MMOGs. They are the same thing. There always seems to be some disagreement between designers and users regarding this. Raph observes that designers (and most people who have worked on MUDs) see them as the same. Players, especially players of only one type, don't. The post goes about defining the simulation as run by a server, and the client as a filter for the streaming data. The back end, while increasing in complexity, has not really changed all that much since the first days of the text MUD. The client may be 3D, real-space, or text descriptions, but it all comes down to representing the data available from the server.
Very conclusive. An excellent definition of a what the MMOG (or MUD) client is and does.