Parts of the muttiverse are self-contained (they have no contact with other authors' worlds), but some, notably any planets or peoples involved in the Twine Wars, are connected to other authors' worlds.
All of Mutt's worlds that are connected to the Twine Wars, or otherwise involved with off-world contact (such as visits from other Pro characters), exist in a single, infinite universe (at least, not finite for our purposes here). There's no system of parallel universes or 'shadow' (as in Zelazny's Amber books); if you can get to it by any means, you could also get to it in a fast enough spaceship.
Such of Mutt's characters as can teleport are assumed to move around in a single universe. In Perry's case, she can visit other universes in the same way, but in order to do so she has to have been to the place before or be shown detailed enough directions in a form she can understand. Demonic keys can only move between already-existing nodes.
There is also a hell/heaven duality, which does not feed off any of these three worlds, but has its own storyline and continuity and characters who cross over occasionally with Mutt's Twine Wars worlds.
Shade is a planet geologically similar to Earth (at least until Mutt throws some originality at it). It has five major sapient species (all humanoid) and magic, lots of magic.
Genetically: genetics are weird there, they don't exactly have DNA and there is a higher incidence of mutation during certain parts of the reproductive cycle.
Magically: Shade runs a highly sophisticated implementation of Mutt's magic system, and really gets its technical act together during the later stages of the War as a result.
Wildlife: there are a few twists on 'fantasy' animals, such as rat-deer-like unicorns. There are also dinosaurs, especially marine ones. There are huge intelligent dinosaurs living at the poles, but that's nobody's business. See Fauna of Shade.
Instar is effectively a half-sphere, because its 'equator' features some kind of barrier impassable to people, mages, airships, trains etc. Its 'years' are 30 Earth years long and 'orbit' the planet (such that summer and winter travel around once every 30 Earth years).
Socially: There is a single sapient species, which is unusual in Mutt's writings. The city is stratified into commoners and aristocrats, the latter term meaning exactly the same as 'politician' in this context. There are also non-citizens, who are found, as the term implies, in the colonies rather than in the city. Gender is somewhat different there.
Religiously: Gods exist and intervene. These have priests and religions, but also avatars and elect walking around. They even hire monastic assassins for their own purposes. The various religious orders in the city hold no official power, but the Mercies do have very capable operatives for intelligence-gathering and are made use of by politicians.
Wildlife: All megafauna have been brought under control, and the only large animals commonly seen are domesticated. Their taxis are pulled by ostriches, and what machinery isn't water-powered (they have an odd source for this) tends to be ox-driven. See Fauna of Instar.
fuzzworld will have a sensible name only when aliens bestow one. Its inhabitants don't see any need for a name for an entire world, you see. It features a lot of dense jungle teeming with animal and plant life, a lot of it very dangerous. That, and the lack of any obvious mineral wealth, is the reason it hasn't been conquered yet.
Imago. Introduced partly to stir up Instar, which may up until Imago's appearance have been maintaining neutrality (depending how things go, of course).
Pancharon, list of Mutt topics