Despite the names implying some form of fundamental difference, Overfolk and Underfolk come from the same place and are really the same "species", or whatever their dimension (referred to as the "Outside")'s version of a species is. Underfolk left their dimension due to attempts by Overfolk, a dominant militaristic culture, to eradicate them, and some Overfolk have followed them to continue this campaign. The dimension the Folk come from is incomprehensible to humans, being essentially made of pure energy, but Folk maintain connection to it and can draw energy out of it, allowing them to essentially add matter to and alter their bodies. Folk have been on Earth for most of human civilization.

Underfolk

Underfolk usually alter their appearance to imitate animals; families tended to pick a specific animal to mimic when they first traveled to Earth, and animosity has formed between different Underfolk families due to these initial divides. There has been a movement, especially by younger Underfolk, to form connections with other clans due to increased persecution from human governments (when previously they had enjoyed obscurity) as well as advancing technology making it easier for Overfolk to mobilize. Underfolk are the source of folklore regarding talking animals and shapeshifters, a common motif across many cultures and societies.

Overfolk

Overfolk have no desire to blend in on Earth and rather than using energy from their home dimension to create normal seeming matter, they simply convert it into a sort of "solid light" which forms weapons. They also form celestial-appearing wings out of this light energy which they can use to fly. Overfolk can also use light originating in our dimension for this purpose, but they generally do not (with a few notable exceptions). As mentioned previously, they are dedicated to eradicating Underfolk and have been for as long as living memory. In the present day it is more out of a sense of tradition and spite than anything else, as the initial reasoning (or lack thereof) has been lost. Overfolk are the source of the conception of an "angel" and can thus be inferred to have mainly operated out of a narrow region before spreading over the centuries.

Demons form outside of a structured dimension, in a kind of "primordial darkness". Demons therefore do not have a home dimension, as they only "exist" in any meaningful sense as leaks into other dimensions. We don't know how a demon would manifest in the Outside, but in the Inside they take the form of shadowy figures with undefined shapes which do not seem to obey physical laws, being able to teleport and not having any sort of mass. They are often malicious and have the power to cause horrific visions and nightmares as well as simply kill humans outright if the human does not have a magical defense, usually via heart attacks, although sometimes the human in question will choke on some sort of unidentifiable ink-like substance which fills their lungs. While it was long thought that demons were inherently and unchangeably malicious, one—or perhaps two, depending on your count—exceptions have ultimately challenged this.

Demon-Touched Humans

Some humans have survived encounters with demons, usually through some form of magic intervention. These humans often gain powers, which are the closest thing to generic "superpowers" that exist in this universe (e.g. super speed, magic shields, electric powers). When using these powers said humans glow in various colors, although this glow does not appear to be "light" as it cannot be picked up by mechanical sensors or cameras, despite being visible to the naked eye.

Magicians are truly traditional magic users. They use all the trappings of the "wizard" caricature: runes, wands, staffs, secret societies, hidden sanctums. In modern scholarship, magicians are thought to draw their power from another dimension, either the Outside or a yet uncontacted dimension. Said scholarship is conducted by magicians themselves, as they have managed to keep their existence a secret outside of a few scattered cases of a wizard's magic becoming public knowledge, which are assumed to not be indicative of such a large body of magic adepts. Magicians form "houses", essentially clubs of magic users which share extra-dimensional sanctums which can be entered through a summoned portal with a special pass-code. These houses are invite only and most have consisted of the same set of families going back generations, with new apprentices who are familiar to a member family occasionally being inducted. Children exposed to magic from a young age are able to channel it easily, similar to the way children learn to talk through exposure to language. Learning magic at a later age takes more work and while the magician can still achieve mastery it will never come as easy to them as someone who acquired the skill as a very young child. Magicians often work to "banish" or otherwise hinder demons and take demon-touched under their wings, although the powers demon-touched have are fundamentally different from other forms of magic in their properties and are not learnable.

Although their name can obfuscate this, "Outsiders" do not originate from the dimension called "The Outside" but rather from Outside the Universal Layer Cake altogether. Outsiders are residents of the Universal Layer Cake, usually humans although there are a few examples of Folk Outsiders, who become "corrupted" by an extra-extra-dimensional entity called Echidna. They begin exhibiting monstrous characteristics, such as their flesh turning to stone or diamond, growing extra eyes, mouths, and other body parts, and otherwise warping to become monstrous inhuman creatures. During this process their minds and humanity will degrade before Outsiders eventually "exit the time stream", whereupon they begin appearing at random points in the past and future and wreaking havoc. (This means that it's possible for a pre-change Outsider to encounter themself in the past.) Most Outsiders are violent and animalistic (although not necessarily malicious as they do not seem to be lucid and aware of their actions), but some seem to still be conscious and aware of themselves, capable of speech and thought. These Outsiders can be reasoned with, although usually they are still somewhat maddened and irrational. 

Echidna

Echidna, named after the mythological mother of monsters (by humans as she herself does not have a name), is the creator of Outsiders and is able to communicate with humans mentally. She is fully conscious and calm, is able to perceive all of time and space at once, and mainly creates Outsiders as a form of entertainment for herself. She is incapable of being reasoned with and sees humans as playthings, but she never acts out of spite and is impossible to insult, so many humans are able to have reasoned, enlightening conversations with her once they understand who she is and accept the premise that she will not change her actions or respond to moral arguments.

"Preter" is a generalized term used by the public to refer to any kind of "extra-normal" or "preternatural" phenomena. Because it is a term used by laypeople and has been increasingly politicized in its use by a government and societal landscape seeking to other, suppress, imprison, and murder anything deemed a preter, it is overgeneralized and lumps disparate and unrelated people and supernatural monsters into one category. Many people included under this umbrella have distaste for it both for its derogatory origin and use and its over-inclusion of people and entities with zero relation to each other, but some preters do identify with the word, usually due to a lack of connection to a specific cultural group associated with their powers which they can use as an identity label.