There have long been Sabbatarians in North America, beginning from the time before the United States was a country and people fled Europe to escape religious persecution. However, Sabbatarianism stayed mostly under the radar until the late 19th century when William Miller began to predict the return of Jesus Christ in 1843 – 1844.
However, Miller himself was not a Sabbatarian, nor were many Adventists back then (the name “Adventist” only later became a shorthand for “Seventh-day Adventist”). From this common background came the Church of God (Seventh-Day) and the Seventh-day Adventist Church. However, it was not overnight, and it turns out that the SDAs were originally against any form of church structure at all, viewing authoritarian government as one of the hallmarks of Babylon.
You can read more about this and where our common heritage with the SDAs lie, as well as some of the main reasons for the groups separating in “How the Seventh-day Adventist Church came to be“.