"I'm Presbyterian," Trump said at a rally in Florida on Saturday. "Boy, that's down the middle of the road folks, in all fairness. I mean, Seventh-day Adventist, I don't know about. I just don't know about."
Carson, who earnestly committed himself to the church when he was 14, is perhaps the faith's most famous member.
Trump later said that he wasn't trying to "send a dog whistle" to religious conservatives who might look askance at Adventist doctrine. "All I said was that I don't know about it," he told ABC.
Fair enough. A lot of Americans don't know much about the Seventh-day Adventist Church. The Protestant Christian denomination turned 150 years old in 2013, which makes it a relative newcomer on the religious scene. (This is year 5776 in Judaism, by contrast.)
Many Adventists embrace their outsider status, calling themselves "God's peculiar people." But Carson, while acknowledging that people tend to ascribe "any weird thing" to Adventists, has played down the differences, saying dogmas and rituals are not his cup of nonalcoholic beverage. (Adventists don't drink or smoke.)
In any case, if you're like Trump and need a quick course on Adventism 101, here are three beliefs they share with mainstream Christians, followed by several unique to Seventh-day Adventists.
One quick caveat: Not all of the 1 million Adventists in the United States and estimated 18 million worldwide ascribe to all of the church's beliefs in exactly the same way. Like all religions, Adventists display a range of intellectual diversity and the faith itself has evolved over time.
1. Adventists believe the Bible is the infallible word of God
Like conservative evangelicals, Adventists honor Scripture as an unquestionable source of wisdom, inspiration and guidance. "In this Word," the church says, "God has committed to man the knowledge necessary for salvation."
Many Adventists also believe the Bible offers a historically accurate view of ancient times, which is why Carson, for instance, ascribes to Creationism, the idea that God created the world in six days.
2. Adventists believe sinful humans can be saved by Jesus
No surprise here; every Christian denomination believes this. Adventists, like other Christians, also believe in the two other members of the traditional Trinity: God, the father, and the Holy Spirit. Salvation comes through the repentance of sins and holding faith in Jesus, but grace is ultimately granted by God alone, the church believes.
3. Adventists believe the Bible counsels against abortion, same-sex marriage.
Again, this is similar to Catholics, evangelicals and many conservative Protestants.
While many Adventists keep their distance from partisan politics and try to maintain a wall between church and state, the church has spoken out against the June Supreme Court ruling that legalized same-sex marriage in the United States.
The church's official position on abortion is nuanced, respecting the consciences of women who decide to terminate a pregnancy under "exceptional circumstances." However, the church states, the Bible clearly "calls for the protection of human life" especially "the weak, the defenseless, and the oppressed."
Unique Adventist beliefs
1. Adventists worship on Saturday, the "seventh day"
The Hebrews in the Old Testament worshiped on Saturday -- the sabbath and seventh day of the week, according to the Jewish calendar. Jesus, being a Jew, also attended religious services on Saturday. And both of those examples, Adventists say, are good enough reasons for their church to worship on Saturday.
Adventists keep the sabbath holy by resting -- as God did on the seventh day, according to the Bible. Many typically do not work, attend funerals or participate in "secular" entertainment from sundown on Friday until sunset on Saturday. (Carson apparently believes campaigning is permitted, though.)
2. Adventists do not believe in an eternal hell
Unlike many other Christians, Adventists don't believe in a hell filled with lakes of fire and eternal torment. That's mostly because the church does not see such a place literally described in the Bible, explained Douglas Morgan, a professor of church history at Washington Adventist University. When Jesus tells the story of the rich man in Hades, he is speaking metaphorically, Adventists believe.
Adventists also argue that a good God would not condemn his people -- even sinners -- to never-ending punishment. In the church's view, the dead sleep in the grave until the second coming of Jesus, when he will judge the living and the dead. Good people go to heaven; bad people are just -- poof -- annihilated.
3. They do believe that Jesus' second coming is imminent
Speaking of the second coming, many Adventists believe that it's going to happen soon, and some are chagrined that it hasn't happened yet. When the denomination celebrated its 150 anniversary in 2013, some church leaders were downright disappointed that their church had lasted so long.
"If you took a time machine and visited our founders in May 1863, they'd be disconcerted, to say the least, that we're still here," David Trim, the church's director of archives and research, said at the time.
4. Adventists believe in the visions and prophecies of Ellen White
It's rare for American religions to have been co-founded by a woman, and rarer still for the faith to revere her as a prophet -- but Ellen G. White was no ordinary woman.
White, who died in 1915, claimed to witness a series of some 2,000 visions, some about the Bible, others about more mundane topics such as healthy diets. Many of these revelations were incorporated into church teachings, which has led some other Christians to disparage Adventists.
Morgan said that Adventists believe the Bible is the final authority and that White's writings are a "lesser light pointing to the greater light" -- that is, Scripture.
Canonical or not, White teachings on health seem to have been effective. Adventist Health System is one of the largest nonprofit hospital systems in the country, and studies conducted by the denomination have found that their healthy lifestyles have led to longer lives, on average, than other Americans.