Peyote supports two well documented religious traditions that are not versions of each other, and conflating them is the most common error made about it.
The Huichol, or Wixarika, of the Sierra Madre Occidental undertake an annual pilgrimage of several hundred kilometres to Wirikuta, the high desert where the cactus grows and where they hold the world to have been created. The journey is a return to a place of origin, the pilgrims take on the identity of the ancestor deities for its duration, and the peyote is hunted rather than gathered, addressed and shot with an arrow as a deer. The association of deer, maize and peyote as a single complex runs through Huichol art and ritual and has no counterpart further north.
The Native American Church is a different thing: a Plains ceremony that spread rapidly in the late nineteenth and early twentieth centuries among peoples who had not previously used peyote, incorporating as a church and taking on Christian elements to varying degrees. The all night meeting is held in a tipi around a crescent altar and a fire, with a water drum, a gourd rattle and a staff passing around the circle, and it is directed by a roadman. Its purposes are healing, sobriety and community.
Both are living. Neither is the origin of the other. The Huichol tradition is the older and the more localised; the Plains ceremony is the more widespread and the more institutionally organised.
Sources Flesh of the Gods: The Ritual Use of HallucinogensPeter T. Furst (editor) with Peyote Religion: A HistoryOmer C. Stewart