A multiple-user dungeon (MUD) is a textual cyberspace that can be explored by dozens or even hundreds of participants, who can explore the virtual space and interact with each other.
A MUD Object Orinted (MOO) allows participants to add to the virtual space (following the protocols of object-oriented programming). Participants can create their own virtual rooms, populating them with props and NPCs.
Classic IF, which focus on puzzle-solving and discovery, does not allow multiplayer interaction (simply because networking technology was too arcane and expensive at the time). Some of these classic IF features may be present on MUDs and MOOs, but a visit to a MOO is likely to involve wandering around aimlessly chatting, rather than lookiing for puzzles to solve or a narrative to experience.