Sounds like someone with authority needed a scapegoat for why kids turned up exsanguinated.

Fae are from Farie. Get your white cultural history straight.

The empire of mankind must lay exterminatus upon the xenos mutant threat.

Tolkien and Barrie popularized faeries of varying kinds in pop culture.

Pixies/Hobbits/Dwarves/Elves/Giants/Ogres/Trolls/Goblins/Imps/etc.

A introduced significant changes to them, and these changes were further altered as culture went on.

Hobbits were inspired by domestic faeries like brownies, these were a subtype of Dwarves, who were themselves a subcategory of Elves.

Goblins were also Elves, the name literally translating to "ugly elf", the take on them that they were Elves who were corrupted is actually quite compatible with the mythology.

Tolkien included various folkloric takes on the same creatures, using multiple names for them as well, pop culture simply did the logical thing and made the larger versions "orcs" into a different category altogether.

The smaller winged varieties of faerie, which are often simply referred to by that name (notably after after hoax of the "cottingly faeries"), can be subdivided into pixies, of which the likes of Tinkerbell is a good example (the name derives from the popular characterizations of pixies as to do the type of work such as tinkering with bells), sprites are another type, the name derived from the word "spirit" and "sylph", as they are commonly associated with the wind (similar to how Dwarves are associatedwith earth, Dwarves and gnomes were originally the same kind of faerie), sprites were typically fond of mischief like turning invisible and living in the beards of old men who grew their facial hair our too much.

The darker smaller statured faerie (with or without wings) is the "imp", who was known to scratch at the skin or hair of people and animals and spread disease (the name imp derives from the term referring to small branches, a reference that is made due to the aforementioned scratching behaviors), christianization of pagan myth would later associate imps with being demons rather than faeries (similar to what was done with satyrs and other goat spirits in the making of the popular image of the devil).

Tolkien divided Giants, Trolls, and Ogres into separate species, similar to what was done with household faeries, Dwarves, and Elves, they were also originally synonymous creatures as well.

The physical descriptions of the faeries mentioned was standardized with these works of popular fiction, originally the appearance of an elf would vary widely from place to place, in some places they'd be described as having inhuman features that would readily give away their otherworldly nature's to humans who saw them, they could not be easily mistaken as human when beheld in their true forms.

The popular depiction of Elves as humans with pointy ears is entirely a creation of Tolkien, who had remained them not as inhuman humanoids, but as humans who had not fallen from grace with God.

Thus they looked like humans, and were distinguishable not by any physical appearance, but by a different spiritual nature, a higher destiny, and the curse of immortality.

I rather liked how fiction like Warcraft and Warhammer had brought Elves closer to their mythological roots by making them have a more clearly inhuman appearance, rather than just being humans with pointy ears.

The divide between dark and light Elves was originally of norse myth, and had them come from different realms from one another, in Tolkien, the distinction was whether they had gone to the lands of light and seen the simarils or whether they had either refused to make the journey or failed to do so, choosing mortality over eternal life.

Wagner had been the first to make Dwarves distinct from Elves in his work on the opera of the ring of the nibeljung (which served as a source of inspiration for Tolkien along with the greek myth of the ring of gyges), the Dwarves were the titular nibeljung who lived in nibelheim, and the focus was on one who very much fit the description given by Tolkien of how Dwarves were which remained popular in media to this day.

Hobbits, the household faeries like brownies, were known to bless those who followed their rules, and aid around the house, but were also known to curse or do mischief to those who offended them.

One example of the latter was the buttery spirits, who would spoil the butter of the family that refused to pay them proper appreciation for their work.

Some mythology made a distinction between the household fae who did good and those who did bad, making the latter just evil spirits who acted out of malice rather than to teach a lesson.

Giants Trolls Ogres, these were said to dwell in rarely visited and obscured places, like in caves, or mountains, or under shady places, or in rivers, or in dense forests, or abandoned castles and ruins, if it's had to get to, hard to see what's there, and dangerous to visit, it's likely that a large brute faerie of sone kind is making that place its home, and perhaps guarding it's territory, they were often eaters of men, and repulsive to behold in some way.

It was a good way to keep people wary of such places, abd keeping to areas that are visible, well populated, and widely traveled, so the myths were of utility for a more primitive civilization of humans living in a much more dangerous world.

Ogres were frequently described as being more bestial in appearance and manner, a notable subcategory were the ettins, who had multiple heads and possibly also additional limbs (likely inspired by the titans of Greek myth, such as the hecatoncharys), Trolls, when illustrated by artists frequently took a similar appearance to modern goblins (large noses and ears that stick out, mouths full of sharp teeth, etc.) Trolls were said to turn to statues in the sunlight, and use their noses to sniff out the blood of a baptized Christian.