We have a somewhat clear "cosmology" in WoT: Creator and Dark One are both "proven" to exist (via channeling and Trollocs, respectively). These two forces are antithetical to each other, yet drive the course of human history.

Mashadar and Machin Shin are both apart from the Creator and DO, and are both antithetical to the Creator and the DO. They also have more in common than starting with the letter "M." They are both evil entities that have "sprouted" and "flourished" - while being different from - their original sources. Let me expound...

In the case of Mashadar, an extremely-intense human evil gave birth to a malevolent spirit that corrupts and destroys every living thing it touches. Machin Shin, on the other hand, seems to be a creature that "spawned" from the gradual, centuries-long effect of the DO's Taint on the Saidin that created the ways; it too corrupts (petrifies) and destroys every living thing it touches.

In each case, something evil gave birth to a new evil - an evil that would destroy anything, including the same things (people of SL, male channelers) that brought them into existence. Both seem born from madness; in the case of The Ways, it's the literal madness of DO-tainted Power, while it's metaphorical in the case of Mashadar (the anti-evil fervor of the SL populace). Neither has a truly physical presence (e.g., fog and wind), but they can affect physical things. Neither truly recognizes any master (neither tainted male channelers nor people of SL). If you're familiar with the scientific term "tropism," you can see how they behave similarly.

Tropism just means that a creature is drawn to something. Many plants will "shift" the way they grow in order to "stretch towards" a light source - that's being phototropic. Some bacteria will grow so they reach toward their own sources of nourishment (e.g., sugars and water?). This is the same kind of thing that makes tree roots grow in the direction of more minerals and H20.

MS is drawn toward living things when they are in The Ways. In the case of Mashadar, it too was drawn toward the presence of living things that walked inside its borders.

Machin Shin is a relentless, thought-less (?), and possibly-eternal destructive monster. So is Mashadar. The nature of each evil is very similar, because something that was bug-$*%^ nuts was involved in each case.

Fain was only driven by the DO's evil (and his own anger) at the first novel's start. When he MERGED into the evil of SL, he became something new and different; yet he'd already been mad given what happened in the next part of tEotW (when his DO-caused compulsion to follow the Taveren Three drove him like a slave).

Like Machin Shin and Mashadar, Faindeth/MorPadan seems to be an evil spinoff who is crazy and willing to destroy anything and everything. The new Fain sounds like he has a lot in common with Machin Shin, so it makes sense that the insanity of MS would "relate" to Fain's nature. This is especially sensical since MS obeyed principles of "tropism" in the first place - it was drawn to a living thing, only to realize that it was something similar to itself.