"I've realized where my success has come from, and I don't in any way deny my faith in God," Carson told reporters at a campaign rally in Anaheim, California, when asked about the biggest difference between him and the Republican presidential front-runner. "And I think that is the big difference."

"By humility and the fear of the Lord are riches and honor and life and that's a very big part of who I am," said Carson, paraphrasing a Bible passage. "I don't get that impression with (Trump.) Maybe I'm wrong, but I don't get that."

Carson, who is a Seventh Day Adventist, has made faith a cornerstone of his campaign message. Powered by the backing of evangelicals, Carson is polling highly in Iowa, a state where about half of caucus-goers this winter are expected to be born-again Christians.

Trump's, a tough-talking New Yorker who made his fortune in real estate, is not known for harboring deep religious beliefs. He's said earlier this summer that he's never sought forgiveness from God, and then referred to communion as "my little wine and my little cracker."

But the Republican is increasingly sharing elements of his faith. Trump, identifying as a Presbyterian, has started to regularly say on the campaign trail that the Bible is his favorite book -- though he declined to share his favorite verse when asked by a reporter last month.

That has not sunk Trump's standing with evangelicals, however, who still support him by a wide margin. But in Carson, Trump may be encountering the most able critic of his religiosity.

RELATED: Church says Donald Trump is not active member

A prominent neurosurgeon and author, Carson has climbed to second place behind Trump in some GOP polls, and recently topped a Monmouth University survey that showed he had more evangelical support than did Trump. Carson blasts Planned Parenthood, which provide abortion services to women, on the stump, and has made expanding religious liberty a central part of his pitch.

"Millions and millions of evangelicals didn't vote," Carson said of the 2012 election. "When you don't vote, you are voting. You are voting for the other side."

Carson's play for these Christian voters could open up a new frontier in his battle with Trump, who Carson also named Wednesday when referring to people "born with a silver spoon in their mouth."

Trump has not sparred with Carson as frequently as he has with other rivals, and Trump has only said he would attack candidates who throw the first punch. But Carson has criticized several of Trump's policy proposals lately. On Tuesday, Carson suggested Trump's plan to deport undocumented immigrants was unrealistic.

"It sounds really cool. You know, 'Let's just round them all up and send them back,'" Carson said at the Commonwealth Club of California. "People who say that have no idea what that would entail in terms of our legal system, the costs -- forget about it. Plus, where you gonna send them? It's just a double whammy."

CNN's Maeve Reston contributed to this report.