MUDs and MOOs
A Multi-User Dungeon/Domain. The term MOO is an extension of that, standing for MUD, Object Oriented.
A MUD or MOO is run by a server, typically written in C for maximum portability, but occasionally written in other languages, such as perl or python.
Multi-user, text-oriented games generally fall into two categories, both of which are quite similar to each other as well as to interactive fiction games.
MUD is the generic name for the older of the two types of games. It is an attempt at a D&D-style hack and slash environment. Players group together to kill monsters and gain experience. MUD parsers tend to be of the extremely limited, two word variety. They only cover the bare essentials required for the genre (though what they do cover is rather thorough). Nonetheless, several do have simple IF-like puzzles. Various IF games, such as Magocracy, have been heavily influenced by this sort of MUD.
MU*s, on the other hand, stress character interaction, roleplaying, and most interestingly, world building. Unlike in MUDs or IF, the world is dynamic, and players can add to the environment. They can create rooms, objects, rudimentary verbs, and highly-complex programs. Many MU*s have fairly sophisticated NPCs with which players can interact.
The key to these games remains interaction. Unlike IF, and despite game-like or world-building features, the most important interaction in these games (and what makes them interesting) is player to player, rather than player to world.
IF aficionados may want to check out ifMUD, Guncho, and Seltani.