A MUSH is an online game similar to MUD. They are similar to text adventures. The difference between a text adventure and a MUD is that a MUD is a multi-player system. Players fight, gain experience, and when they reach wizard level, they can start coding new quests. On a MUSH, coding is even easier, and much less emphasis is placed on combat and experience. Basically a MUSH is as simple as possible, technically. Everything else is coded by players, and usually gaming involves almost no technical features except for talking and posing in in rooms.
(The rest is not relevant.)
The critical difference between DreamStones and a MUSH is that a MUSH resides on a single server. Therefore there is a God King that can switch off the server. There's also bandwidth, hardware, and maintenance costs to bear. The distributed nature of DreamStones is supposed to take care of this.
Another difference would be that DreamStones is graphical and TileBased, which can lead to different edition dynamics. Not being text-based may make quite a difference (less freedom, easier suspension of disbelief …). Apart from those, I guess DreamStones could be considered as a GraphicalMUSH?.
(More analysis should come here, I guess.)