Throughout his 16-year political career, the 57-year-old Indiana governor has adhered to traditionally muscular Republican policies on foreign affairs.
Trump, however, has taken a more isolationist approach and placed less emphasis on foreign issues. The issues that he has put at the center of his campaign are largely the ones he and his running mate disagree on.
Trump made his opposition to the Iraq intervention a major theme, criticizing Democratic opponent Hillary Clinton for her 2002 vote backing the war when she was in the Senate.
Pence backed Iraq war
Pence, near the beginning of his 12-year tenure in the U.S. House, voted for the resolution authorizing the 2003 Iraq invasion as well.
Pence, who chaired the House Foreign Affairs subcommittee on the Middle East, was also a prominent backer of the 2007 "surge" strategy sending more U.S. troops to the faltering effort in Iraq, telling CNN's Wolf Blitzer at the time that "the surge is working" while also defending the original decision to invade despite the absence of weapons of mass destruction.
Pence has also struck a harder line on Russia than Trump, whose authoritarian president, Vladimir Putin, the presumptive GOP presidential nominee has praised.
Trump asked an audience at a California rally in May, "Wouldn't it be nice if we could get along with Russia? Wouldn't that be nice?"
Pence has opted for stronger rhetoric, telling the Conservative Political Action Conference in 2015 that, "A new Iron Curtain is descending down the spine of Europe as modern Russia seeks to redraw the map of Europe by force."
He added, "Putin's Russia ignores talk of sanctions, claims land and supports rebels in Ukraine with impunity."
And Pence has previously taken issue with some of Trump's national security proposals, calling his proposal to ban Muslim foreigners from entering the U.S. "offensive and unconstitutional" in a December tweet.
Trump has since refined the proposal, saying it would only apply to citizens from countries with connections to terrorism.
Opposing views on trade
Perhaps more than any other international issue, Trump has made global trade a defining aspect of his campaign -- yet Pence has taken a diametrically opposed position.
The real estate mogul has frequently called NAFTA, which regulates trade between U.S., Canada and Mexico, "a disaster." During a Republican primary debate in February, he declared, "We are killing ourselves with trade pacts that are no good for us and no good for our workers."
Pence, in contrast, praised the role of global trade and slammed protectionism in a 2010 speech to the Detroit Economic Club.
"Protectionism and closing our doors to other countries does not help us, or people in the rest of the world," he said. "We must support expanded free trade to renew American exceptionalism and create jobs."
Pence also backed free trade deals with Panama, Colombia and South Korea while in Congress.
Potentially most problematic for Trump, Pence has been a strong proponent of the Trans-Pacific Partnership, a regional trade deal involving 12 countries pushed by the Obama administration.
"The Trans-Pacific Partnership is another disaster done and pushed by special interests who want to rape our country -- just a continuing rape of our country. It's a harsh word, but it's true," Trump said in a speech last month in Ohio.
But in a September 2014 tweet, Pence gave the deal a ringing endorsement and called for its "swift adoption."
However, the Indiana governor has found common ground with Trump on some national security issues -- especially when it comes to criticizing President Barack Obama.
Like Trump, Pence has slammed Obama for reductions in the size of the American military.
Shared stances on the size of the military
"This administration has reduced our Army, now its smallest size since 1940. The Navy has fewer ships than at any time since 1916, and our Air Force has its smallest tactical fighter force in history," Pence said at the Conservative Political Action Conference.
Trump made similar statements in an April foreign policy address.
"Our active-duty armed forces have shrunk from 2 million in 1991 to about 1.3 million today. The Navy has shrunk from over 500 ships to 272 ships during this same period of time. The Air Force is about one-third smaller than 1991," Trump said.
The Indiana governor has also echoed Trump's critique of the President's preferred terminology for terrorist groups.
"Lecturing the American people about the crusades while refusing to call Islamic extremism by name is an abdication of leadership," Pence told CPAC.
They also largely agree on Israel -- nowadays.
Pence is an avid backer of the Middle Eastern ally, telling the CPAC audience, "Israel's cause is our cause" and voicing approval of the decision by then-House Speaker John Boehner to invite Israeli Prime Minister Benjamin Netanyahu to address Congress to lobby against the Iran nuclear deal the White House was then negotiating with Tehran.
Trump has also blasted the deal, and has recently staked out an aggressively pro-Israel stance.
"Israel is a very, very important ally of the United States and we are going to protect them 100%," he said last week, rebuffing an audience member's criticism of the country.
But last winter, Trump was castigated by many Republicans for declining to promise to keep Jerusalem as the undivided capital of Israel. He also said peace would depend on whether Israel is willing to make sacrifices and that he would remain "neutral" in negotiations.