"Trump is looking to be challenged by other people. He's not looking for 'yes' people around him," Priebus told CNN's Jake Tapper on "State of the Union," explaining the Pence pick.
"I think that shows a lot of maturity. I think it shows an understanding of an electorate and an understanding of what it takes to defeat Hillary Clinton," Priebus said.
The clearest evidence of their split comes on the Trans-Pacific Partnership. Trump called the 12-nation Asia-Pacific pact negotiated by President Barack Obama's administration a "rape of our country."
Pence, meanwhile, has lobbied for its passage.
Asked about the differences between Trump and Pence on trade, Priebus said it's an issue that divides the GOP.
"You'd be surprised. This is a split issue in our party. Not everyone is crazy about TPP. I can tell you, these delegates aren't crazy about TPP. I can tell you a lot of the base in our party isn't crazy about TPP," he said.
Tapper responded: "Yeah, but your vice president is."
And Priebus said: "Listen ... not as wildly crazy as you might think."
The GOP chairman insisted that having two candidates share a ticket that have diverging opinions on TPP is "not some stunning, startling" reality.
Then, after answering another question, Priebus circled back.
"By the way, when you said 'your VP,' I thought you were talking about Paul Ryan ... I wasn't sure you were talking about Pence," the RNC chairman said, as he tried to explain his previous response about the trade divide.
Then, Priebus also sought to brush off the differences in position as a general disagreement within the party.
"His strength and his negotiating ability and his desire to do better is his most important position on trade," Priebus said of Trump.
Priebus downplayed other differences between Trump and Pence, as well. Asked if the Republican ticket would have supported the Iraq War -- which Pence backed in Congress and Trump has said he opposed -- he said: "You'll have to ask them."
And on Trump's proposed temporary ban on Muslims entering the United States, Priebus insisted that Trump's position has evolved to a more targeted ban on travel from countries that are terrorist safe havens, and has nothing to do with religion.
Pence, who'd initially called Trump's proposal "offensive and unconstitutional," backed Trump's updated position in an interview with Fox News after being selected as Trump's running mate.
"I am very supportive of Donald Trump's call to temporarily suspend immigration from countries where terrorist influence and impact represents a threat to the United States," Pence said.
Pence added: "What I've heard from Donald Trump, and I believe the position he's articulated that resonates with millions of Americans, is that we've got to find out what's going on, and we've got to do something different, and we've got to put the safety and security of the American people first."
Priebus also denied reports that Trump was waffling over his selection of Pence late Thursday night, even after he had called Pence and offered him the vice presidential nod.
"I spoke to him, I mean, multiple times that day. I know what he was thinking," Priebus said. "He was with Pence, he knew Pence was the right pick, and that's where his head and heart were at."
Priebus, in an interview on ABC's "This Week" with George Stephanopoulos, again downplayed differences between Trump and Pence, this time over Planned Parenthood -- which Pence has previously said he'd support shutting down by having the federal government defund the organization.
"Most Americans agree that federal money, their tax money, shouldn't be used to help pay for abortions. And so that piece alone is something the American people are with us on," Priebus said.
"As far as whether Planned Parenthood, you know, provides, you know, contraceptives or things like that, that's something that gets in the middle," he said. "But I think you focus in on that, I think most Americans are with us. But they also look to the top of the ticket."
In an interview on "Fox News Sunday," Trump campaign chairman Paul Manafort conceded that "this team is not going to see eye-to-eye on everything."
"Trump never said he wanted a 'yes' man as vice president," Manafort said. "He wanted somebody who was experienced, someone who was successful and someone who could help him achieve the objectives in Washington. Gov. Pence does that."