There's many interesting lists of so called 'native American names for Bigfoot' that include things such as ghosts, gods, dwarves, and what most would describe as the 'living dead' or things of that nature, alongside well-intentioned generous translations of words in many now-rare languages that have been perpetuated for years ('hairy man' where 'ogre' might have been better used ect). To be specific, I do mean just things that could be described as 'wild men who live in the wilds, generally larger than a human' instead of any number of innumerous creatures that exist within many Native American belief systems, such as dwarves.
To use a example, the Thunderbird appears among the mythologies of dozens of Native belief systems as widespread as what is now the Southwestern United States to above the Great Lakes; there's many names for it, and outside the realm of speculation regarding possible oral histories of extinct megafauna there's no serious debate that the Thunderbird is 'real'. Meanwhile, stories of 'hairy men/night people/bush indians/wood people' (to use common English translations of a few different creatures, such as the Nuhu'anh and the Ba'wis) generally appear in most large ethnographies of tribes in the Pacific Northwest and elsewhere, but there doesn't seem to be any good research or texts available regarding considering the 'hairy man' as a /universal/ figure in these respective mythologies and belief systems akin to, say, a flood myth.
I am unclear about the question/confusion here. Bigfoot is part of indigenous folklore, occupying a place in indigenous belief systems: there are stories about bigfoot (with various names) and there was a belief that they existed. Both are expressions of folklore.
In addition, Bigfoot has entered modern North American folklore in a more widespread fashion, with stories and belief.
There may be confusion about the idea that folklore means false. That is not the case: folklorists make no judgment about the veracity of a belief: if people tell stories about something, it is part of their folklore. Bears exists. There are native American stories about bears. The stories are part of the folklore.
For something as elusive as bigfoot, there is a question about whether they are real, but real or not, they are part of folklore. Similarly, stories about ghosts can be regarded as folklore, but we do not by that definition assert that survival of death (and communication between the living and the dead) is impossible. Folklorists do not make judgment about the spiritual survival of death by asserting that ghosts stories are folklore. Folklorists are not trained to know anything about the survival of death!
There is a problem with a more judgmental term that is often applied to "other people's" folklore - namely, "myth." That term is best reserved for ancient written traditions inspired by contemporary folklore. By restricting it to ancient beliefs and stories, the word "myth" does not offend anyone.
When using "myth" in a modern context, it has a judgmental tone: "that is just a myth" is much like saying, "that is a silly superstition" - that is, something that should not be taken seriously. Consider the difference between "the Resurrection story" and "the Resurrection myth." Clearly the first is neutral and the second is judgmental. "Myth" is judgmental; "folklore" is not - it is neutral.
I suspect that you are thinking that applying the term "folklore" to stories and beliefs related to Bigfoot is to dismiss such an entity as inherently false - or "mythical." That need not be the case. I have collected stories about bigfoot. I have never seen one, and I do not know if they exist or not. It ain't my job.