The way I have always conceived of cryptozoology is as a grab bag of questions about "hidden animals"...what have people said they've seen? What evidence is there?
(which makes me ask, is there also cryptobotany?)
As long as it is a question about an animal people say they've seen but there is not yet proof either way, I think of any of it as cryptozoology and the creatures as cryptids.
My own involvement has been with the Shunka Warak'in, which I first brought to Loren Coleman's attention as a legend from my tribe back in the 90s, and its connection to a stuffed mounted hyena-like animal that was shot in Montana in the 1880s. A real live hide-and-fur thing. We never thought of it as a spirit, but a regular but very rare animal.
After its inclusion in the cryptozoology oevre, if an animal is proven to exist as a biological species, like the coelacanth or okapi, then it is no longer a cryptid, but is a full-fledged object of zoology. If it is a physical animal, even if it proves to be a case of error in perception or mistaken identity, like most of the so-called "chupacabras" which are really mangy coyotes, dogs or raccoons, or that rotted carcass that washed up on the beach that proved to be a bulldog, then it is still zoology that takes over at that point.
FOR ME, and speaking only for myself, ANYthing that is an animal, or possible animal, can be considered literally within the (remember) -informal- field of inquiry people call "cryptozoology." Hidden animals. Mysteries. Loch Ness monster. Bigfoot. The jury is still out. There are things about these creatures that seem biological sometimes and apparitional or folkloristic at other times. The only reason I haven't rejected Nessie and Bigfoot as creatures of folklore, is because some very believable people swear they have not only seen them, but had close experiences with them. Dr. Jeff Meldrum still is open to the possibility of Bigfoot as an anthropoid biological creature.
However, when you are talking about things that don't act anything like an animal, and seem not to likely be one, like the Mothman or the Jersey Devil, I don't consider those to be part of cryptozoology at all. Very very unlikely. I think a lot of the answers lie not in zoology but in "high strangeness" (another term people argue about and no one can agree on just what it means). I think the answers lie more in the direction of Harpur's Daimonic Reality or Hansen's Paranormal Trickster or Holiday's Goblin Universe or Mangonia, ...whatever those are.
So, as long as an "animal" is apparently biological and the jury is still out on it, I consider it a topic for cryptozoology, which to me, is really a place-holder concept. Once it is proved to be biological, it is no longer cryptozoology, but plain old zoology. If it doesn't seem to be a biological (zoological), REAL, creature, I push it to the folklore end of the spectrum of cyptozoology, which some would reject, and some include. It's not a formal field. It's not zoology. It's just an area of inquiry.