To the extent that Mr. Trump fleshed out his plans for dealing with the North, he said he would put pressure on its neighbor, China, to use its influence with Mr. Kim to curb his nuclear provocations. That is essentially what Mr. Sullivan said in his description of Mrs. Clinton’s policy.

“Putting aside the politics of a different policy, the change would be at the margins, I think,” said Victor D. Cha, the director of the Asian Studies program at Georgetown University. “There is little disagreement that sanctions need to be pushed harder.”

“The main difference between the two might be what would be on offer if North Korea bends to the sanctions and is ready to come back to talks,” said Mr. Cha, who advised President George W. Bush on North Korea. “Trump seems to be saying he would go as far as putting a face-to-face on the table, which would be a break from 30 years of past diplomacy.”

Mr. Trump’s remarks about Mr. Kim reflect less a strategy than his instinct for cutting deals with people. In that sense, they are similar to what he has said about pursuing better relations with President Vladimir V. Putin of Russia. The comments came after Mr. Trump talked about withdrawing American troops from Japan and South Korea, which he suggested should acquire nuclear weapons to defend themselves. Mrs. Clinton and her surrogates have said these statements show Mr. Trump to be reckless, uninformed and unfit to be commander in chief. Still, her aides are sensitive to suggestions that he would be more open to diplomacy with North Korea than Mrs. Clinton, a former secretary of state.

In 2009, Mr. Sullivan noted, she appointed a special envoy, Stephen W. Bosworth, to explore whether there was a serious diplomatic path with North Korea. After Mr. Bosworth left, she named Glyn Davies, who negotiated an agreement in February 2012, known as the Leap Day deal, in which Pyongyang pledged to stop nuclear and long-range missile tests in return for a resumption of American food aid. The deal fell apart after North Korea announced plans to launch a satellite.