CHARLOTTE, N.C. — Four years ago in Denver, Bill Clinton was given the assignment of making the world believe that he liked Barack Obama and wanted him to be president. As one longtime confidant put it, “He had to go out there and say, ‘Yeah, Obama beat the blank out of me and my wife, but still, you should be with him.’“

But that was then.

On Wednesday night here, Clinton will be tasked with a mission that has largely frustrated President Obama: cut through the political clutter and clarify the choice in November. Explain, in his inimitable way, in language that persuadable voters in middle-class America can understand, what Obama has accomplished and why he thinks Obama’s economic policies would pull the nation out of tough times and the Republican alternatives would not.

There is nothing formulaic about Clinton’s presence at the Democratic National Convention this year. He is not just another old presidential war horse being trotted out for nostalgia or a staged show of unity. When Obama called in late July to say he would be grateful if his Democratic predecessor would give the speech placing his name in nomination, something that no former commander in chief has done before, it was an acknowledgment of how much the sitting president needs the former president.

And Clinton, who loves to be needed as much as he needs to be loved, responded with an enthusiasm and diligence that served as yet another signal to people close to both men that an old wound has for the most part healed.

“He is honored that Obama asked him to do it,” said Terry McAuliffe, a former Democratic National Committee chairman. In late August, McAuliffe spent a few days with the Clintons at a beach house in East Hampton, N.Y., and said his close friend seemed obsessed with the convention assignment, continually bringing up books and quotes and ideas he was sifting through.

“This speech is very important to him. He has taken the burden and put it on his shoulders,” McAuliffe said.

The convention speech, which people around Clinton say he is largely writing himself, is part of a full-scale Bill Clinton offensive that includes a series of political ads — now playing in key swing states — that feature the former president offering snippets of the themes he will expand on Wednesday. Obama’s team views this in the most positive light, noting Clinton’s talents and soaring popularity, but history shows the occasional dangers.

In late May, as the Obama campaign was pounding away at GOP challenger Mitt Romney’s role at Bain Capital, Clinton said of the private-equity firm, “I don’t think we ought to get into a position where we say this is bad work. This is good work.” If he was all too public in his critique, it was classic Clinton as campaign manager, sending the message to the Obama team that there are ways to go after working-class voters without alienating the financial industry, a subtlety he mastered during his heyday.

The Clinton-Obama divide four years ago was political and personal. It began during the intense and at times nasty primary campaign between Obama and Hillary Rodham Clinton.

That campaign-season animosity was accentuated by diametrically disparate individual styles. Presidents 42 and 44, separated in age by 15 years on opposite ends of the baby-boom generation, have been called matter and anti-matter, fire and ice, extrovert and introvert.

Clinton could spend five minutes in a Dunkin’ Donuts in Concord, N.H., and meet a stranger whose face and name and life story he could still recall two decades later. Obama spent four introspective years in New York without making a single lasting friend.

Obama seems content to relax late at night alone in the White House residence watching ESPN’s “SportsCenter.” Clinton doesn’t like to be alone and has been known to call a pal so that they can watch a televised basketball game together hundreds of miles apart while on the telephone.

Their differences of style are far less important than matters of substance, although Clinton’s freewheeling exuberance has occasionally troubled the cautious Obama, and Obama’s seeming insularity at times has befuddled Clinton, friends of both men say. In a sense, they start and end in similar places.

When it comes to politics, on most of the big issues, there is little or no space between them as pragmatic liberals, although Clinton was able to craft a clearer ideological definition as a proponent of a new Democratic “third way.”

One former Clinton adviser, assessing the former president’s perspective on Obama, said, “I sense he thinks that Obama gets all the hard stuff right, but doesn’t do the easy stuff at all. And it mystifies him.” Clinton, for instance, was wowed by how Obama put together a successful health-care package, something the former president failed at, yet was confounded by Obama’s inability to go around the country and sell it.

The relationship between Clinton and Obama has evolved in stages. The earliest step toward reconciliation might be the most telling: when Obama, as president-elect, asked Hillary Clinton to serve as secretary of state. She needed persuading, and in this case Obama and Bill Clinton were co-conspirators, both pushing the idea that she should take the job. If there were political calculations involved on either side, the simple fact that Hillary Clinton joined the Obama administration changed the dynamics; that she proved to be indefatigable and adept as Madam Secretary at once heartened her husband and deepened the appreciation of the president.

After two years during which they rarely spoke, the first public sign that Bill and Barack were teaming up on domestic policy issues came shortly after the 2010 midterm elections that proved disastrous for the Democrats, who lost control of the House and barely kept the Senate. Obama found himself making deals with House Republicans even before they took over, agreeing to some tax cuts in exchange for an extension of unemployment insurance.

On the afternoon of Dec. 11, Clinton visited the Oval Office, where he and Obama spent a long session discussing the policy and politics of the situation and how to explain the president’s position. It was, Obama said later, a “terrific conversation” — so stimulating that he thought “it might be useful” for Clinton to share his thoughts with the media and the public. Obama and Clinton seemed like tourists from Des Moines as they scrambled to find out how to open the James S. Brady Press Briefing Room in the White House and then round up enough reporters and cameras to make it worthwhile.

When the scene was finally ready, Obama entered with Clinton at his side. With a smile, he called Clinton “the other guy” as in, “I thought I’d bring the other guy in.” The word “guy” made it a term of affection and respect, marking a change from an earlier time when Obama would more often regard Clinton as simply “the other” — an unpredictable and occasionally hostile alien force.

As Obama stood by, here and there making a point of his own, Clinton let loose with his pent-up insights and formulations on the economy, an issue that he said he spent at least an hour a day studying intensely, adding “and I’m not running for anything.”

With the former president still talking, Obama soon enough excused himself and said he was under orders from his wife to leave for a Christmas party.

Early last fall, with the presidential campaign under way, aides to both men set up another meeting. This one was held not in the Oval Office, but on the links. The two mid-handicap, mulligan-prone hackers talked re-election politics as they made their way around the golf course at Andrews Air Force Base.

But whatever was said that day may have been lost in translation, if not the sand traps. On Oct. 3, two weeks after the golf outing, Clinton held a reunion in Little Rock with a legion of his former campaign troops to celebrate the 20th anniversary of the day he first announced his bid for president, and much of the chatter was about how Obama and his people were struggling, not up to the old standards, unable to explain his presidency. Clinton buttonholed several former aides to make that same lament.

“He talked about how you’ve got to be able to boil it down to a card that people can put in their pocket,” one former adviser recalled Clinton telling him as they sat in the Clinton library. “You’ve got to explain your accomplishments, because it will get lost and people will not remember.”