Wednesday night’s presidential debate did highlight substantial differences between former Massachusetts Gov. Mitt Romney and President Barack Obama. But dig deeper into what they said, compare it to their records, and you’ll find a surprising number of similarities.

Consider the debt. Reducing the debt is a priority for both candidates, and both have acknowledged the worth of some parts of a deficit-cutting plan known as Simpson-Bowles.

During the debate, moderator Jim Lehrer asked Romney, a Republican, if he supports the plan to reduce the more-than $1 trillion federal deficit. Romney did not directly answer the question, saying instead that the president should have grabbed the plan, which called for about $3 in spending cuts for every $1 in new revenue, assuming a full expiration of the Bush-era tax cuts.

Obama, a Democrat, did not fully embrace the plan, though, for a number of reasons, including its steep cuts to the military. Here they agree. Romney has said many times that he will not support military spending cuts. At the debate he said, “I do not believe in cutting our military.”

Second, education. Obama cites investing in education as a way to grow the economy in the long-term. At the debate, he hailed the competitive grant program Race to the Top, which rewards states for raising academic achievement. He said he wants another 100,000 math and science teachers to help educate a more skilled workforce.

At a time when some Republicans have called for eliminating the U.S. Department of Education altogether, and Romney’s vice- residential pick Wisconsin Rep. Paul Ryan has proposed a budget that would slash education spending, Romney said he does not plan to cut funding for schools.

“I’m not going to cut education funding. I don’t have any plan to cut education funding and grants that go to people going to college,” he said at the debate. He congratulated Obama on the Race to the Top program; Massachusetts was one state, in fact, that won the national competition.

Third, health care. Romney said he wants to repeal and replace the Affordable Care Act (though he hasn’t specified how to pay for an alternative), while Obama’s reform prevents health insurance companies from denying coverage based on pre-existing conditions and requires people to buy health insurance or pay a fine.

The matter here comes down to believability, particularly because one of Romney’s finest achievements was his Massachusetts healthcare plan. Romney likes what Obama’s healthcare plan accomplishes, just not the federal mandate, and would prefer a state-by-state approach.

At the debate, he said, “What we did in Massachusetts is a model for the nation, state by state.” We ask, then: What’s the difference? If each state should have a version of Obama’s healthcare law, why shouldn’t there be a federal mandate?

The candidates do have their differences — Romney would make the Bush-era tax cuts permanent, while Obama would repeal them for households earning more than $250,000 annually, and they don’t agree on some social issues, for example — but in important ways their views align.

The respective campaigns will keep emphasizing the sometimes-manufactured differences to make it easier to formulate attacks, and the news media will rightly point out opposing approaches, but look through the rhetoric. For all their efforts to convince you otherwise — at debates and on the campaign trail — they agree on more than you might first imagine.