Every other body in this list was formed by separating from something. The Latter-day Saint claim is different in kind: not that the church went wrong and needed correcting, but that it ceased to exist after the apostolic age and had to be given again.
The movement's own account is that Joseph Smith, a farm boy in western New York, was visited in 1820 by the Father and the Son, told that the existing churches were wrong, and later directed by an angel to buried golden plates which he translated by divine means and published in 1830 as the Book of Mormon, a record of Israelite peoples in the ancient Americas visited by the risen Christ. Priesthood authority was then restored by heavenly messengers, and the church was organised in April 1830.
The historical account differs on almost every point and should be given alongside rather than instead of it. Smith's several written accounts of the first vision differ in detail and the earliest dates from 1832. No plates were examined by anyone outside a group of witnesses, several of whom later left the movement, though most did not retract. The Book of Mormon's account of ancient American peoples has not found archaeological, linguistic or genetic corroboration, and DNA studies of Native American populations show Asian rather than Near Eastern descent; the church's own published essays now favour a limited-geography reading in response.
Smith's later career, the Book of Abraham, plural marriage taught privately from the 1830s, a theology in which God was once a man and humans may become as God, moved the movement steadily further from creedal Christianity. He was killed by a mob at Carthage, Illinois, in 1844, and Brigham Young led the largest body of followers to the Salt Lake valley in 1847.