Cryptozoology is not quite folklore. it's gotten more folkloric over the last 20 years or so, for certain (Dogmen being a prime example of it), but it began as a pseudosciencem and for that, it had to try to be scientific. Part of it is a concept shift, part of it is a language shift.
Old school, proper, published cryptoozology (as oppose to any jerk editing a wiki) is mildly rigorous and has some semblance of standards.
For example, George M. Eberheart laid out 10 types of Cryptids for his encyclopedias of Cryptozoology:
Distribution Anomalies - Animals we know to exist but are living outside their normal range (Big Cats in Britain).
Underscribed, Unusual, or Outsized Variations of Known Species - Kraken, Giant Centipedes, Giant Snakes are all examples.
Survivals of Recently Extinct Species - "I'm not dead yet!" (IE: The Thylacine).
Survival of species known only from the fossil record - We know the animal family is real, but is only known via fossils. IE: Giant Ground Sloths, Dinosaurs, and Pterosaurs.
Lingerlings - Kind of a mix of the two above categories. Creatures from the fossil record who may have lasted a bit longer before going extinct properly.
Animals not known from the fossil record but related to known species - It appears like a regular animal, jut a bit different so it might be a new speices. Or it might not be. The King Cheetah is a good example of it. Some thought it was a new species, but it turned out to be a form of melanism.
Animals not known from the fossil record nor related to any known species - This is where things get weird and more folkloric. The Fresno Nightcrawler is a good example of this sort of thing.
Mythical Animals with a Zoological Basis - The monster isn't real, but it might be based on something real. A unicorn (Rhinoceros) or Manticore (Tiger) are examples of this.
Seemingly paranormal or supernatural entities with some animal-like characteristics - This is where you find the Mothman (some cryptozoologists think it was just a giant owl, while skeptics think it was just a regular owl)
Known Hoaxes or probable misidentifications.
Eberheart explicitly did not count:
Insignifigant creatures - an element of the spectacular is needed.
An element of controversy - it's got to have proponents and skeptics.
Erratics - One off or escapees aren't cryptids.
Bizarre Humans - Supernatural humanoids. Vampires, Zombies, and the like.
Angels/Demons - They are primarily supernatural beings.
Aliens - They are not permanent residence, so they are not counted.
While I don't agree with all of the not-counted (Non-controversies lets us skip the Wallabys in England, the Rheas in Germany, the Giraffes of Mexico, the Cocaine Hippos, Californian Zebras, and Texas Ibex), it's helps illustrate what I'm getting at.
There is some semblance of science around cryptozoology (hence why it is a psuedoscience), it focuses on organisms, and it is not looking at other sapients.
It's not just finding 'evidence' to reafirm a belief. There's a bit more 'ritual' to it.
But I have to ask: can you tell me more about the non-standards origins for La Llarona and the Yuki-Onna?
I mean, as far as I know, the Yuki-Onna story was first recorded by a Greek weeb in Kwaidan.