The difference between Muds and Mushes are distinct, but vague at the same time.
A MUD, is essentially what was a predecessor to a MMORPG. You make a character, level up by killing stuff (usually), get stronger, and so on.
What Muds and Mushes both have in common is they are both multiple user, online, text based games or simulations.
A Mush, as comparative from a MUD, is really, a creative environment. Usually, each player is given tools to create their own rooms, areas, and objectives, as long as it falls in with the theme of the Mush. Some Mushes are more predefined like Muds (whereas only a few, distinct, 'GM's are allowed to build), while some even have no real theme.
I once played on, a few years back, on a Harry Potter Mush. Specifically in the theme of the school, Hogwarts. It was very interesting because you had these diehard fans, hardcore in every sense, playing this mush, and creating this extremely vivid world, filled with Teachers (usually the fans building the world), and with Students (usually guests, or regulars who don't want to be a teacher). It would go on so that, if you took a class, and passed the corresponding test that came at the end of it, you would gain a spell or ability.
That was probably my fondest memory of a Mush, but I don't remember exactly what it was. If you're looking for Mushes or Muds to play, most can be played in the standard windows Telnet client, although to get the most out of them, you're going to want a personalized, color-capable client, such as Zmud. If you want to search for muds, mushes, moos, whatever, the best website I currently recall is MudConnector.com
Hope you have fun in your newfound love, muhaha.
(PS: Most M**s currently exhibit under a 100 players, not at any one time, but overall, a hundred players. So it gets to be really easy to buddy up with all of them, and the game masters and stuff. If you're looking for a game with thousands of players, look towards MMOs or what have you. M**s tend to be for the people who A, can read quickly enough ^_^, and B, enjoy socializing.)
Kayla.