Note that this is in no way authoritative, although it is
reasonably accurate, and it is terribly over-generalized.
This is just a very BASIC document.
History
The term MUD is commonly thought to stand for Multi User Dungeon. Initially written by Richard Bartle, the first MUD servers actually trace their origins as BBS games, with inspiration from the table-top role playing games such as Dungeons & Dragons, as well as other online BBS games such as Legend of the Red Dragon. The basic idea behind MUD servers was to allow multiple people to interact as in a face-to-face table-top game, while exploring and participating in quests and adventures found in the LotRD type servers.
When the various forms of the "Internet" started spreading, MUDs made a natural jump from BBS' to the new 'net. The established servers acquired new blood for design and development, and many variations of the servers sprang up under different design teams. In the late 1980s, the Internet Relay Chat appeared from Finland, further encouraging real-time interaction. In 1989, a new version of MUD appeared -- TinyMUD, written by Jim Aspnes from CMU. It had actually been designed as a front-end for IRC, using the MUD idea of 'rooms' instead of 'channels', and adding in the concept of both things and reserved names with passwords. Instead, it became its own system.
As multiple MUD servers were designed by creative teams, so too did TinyMUD branch off many variations, including TinyMUSH (multi-user shared hallucination), TinyMUCK, TinyMUX, and TinyMOO (MUD object oriented). Largely and very generally, the TinyMUD family was seen as social and social role-playing environments, while the more traditional MUDs -- LP MUD, Diku MUD, UberMUD, and others -- were viewed as the adventure/quest based games that they had traditionally been. There were, and are, many exceptions to that general statement, but by and large the expectational baggage remains.
Much, much more information can be found on the history of MU*s in
general by using the following search terms:
Richard Bartle TinyMUD MUD