Berlin (CNN) There's no secret about which of the two American presidents German Chancellor Angela Merkel is meeting Thursday that she likes the most.

On a day of odd political coincidences, Merkel sat down with one President she calls a friend and with whom she shares a political wavelength -- Barack Obama, and another, with whom she has had a frosty start -- Donald Trump.

Merkel, the most powerful leader in Europe, first met Obama in Berlin discussing democracy and faith at the Brandenburg Gate , meters away from the path of the Cold War wall which once split the city, at an event hosted by the German protestant church.

Then she will be in Brussels where she will encounter Trump at the NATO summit. The current US president didn't even shake her hand in her Oval Office visit in March. So Thursday's meeting will be a chance for a do-over after their odd couple optics during her visit to Washington.

Political contrasts

Merkel's friendship with Obama and awkward early interactions with Trump are a study in political contrasts that the Berlin government and the White House will likely seek to ease given the crucial nature of the Germany-US relationship.

But it seems unlikely that the studious and cautious German leader will ever recreate the chumminess she enjoyed with Obama with the brash and unpredictable Trump.

That easy interaction was on display again on Thursday when Merkel seemed delighted to be sitting down with Obama. The former US leader told tens of thousands of people who showed up to witness their earnest conversation about democracy that Merkel was "one of my favorite partners throughout my presidency."

Merkel once shared hugs and smiles and intimate dinners with Obama as their relationship evolved over the years. In one iconic photo that exemplifies their friendship, Obama sits on a bench while Merkel stands in front of him with her arms outstretched in deep conversation -- with the German Alps in the background.

Obama gave Merkel his nation's highest civilian honor, the Presidential Medal of Freedom, and lauded her as the epitome of freedom itself after she reached the pinnacle of political power in a united Germany after growing up under the political suppression of the communist East.

"The night the wall came down, she crossed over, like so many others, and finally experienced what she calls the 'incredible gift of freedom,'" Obama said at a State Dinner for Merkel in 2011.

Two years later, Merkel poignantly pointed out the route of the wall during an Obama visit to Berlin, and told him that, trapped in the East, she used to listen to trains on the other side and dream of being free.

Contrast such intimacy with the body language on display at the White House when Merkel flew across the Atlantic to get to know Trump.

The President later said that he didn't hear the request and meant no offense but the moment became an irresistible metaphor for the rocky start of their relationship.

JUST WATCHED Did Trump snub Merkel handshake? Replay More Videos ... MUST WATCH Did Trump snub Merkel handshake? 01:02

In effect, Merkel will be coming face-to-face Thursday with one president that she probably wishes were still in the White House and the other, with whom she now has no choice to partner, no matter how tough it is going to be.

Merkel, demonstrating rare sentimentality but also the pragmatic streak that runs through her politics, admitted last year it was tough to see Obama go.

"Taking leave from my partner and friend, well, yes, it is hard. If you've worked together with somebody very well, leave-taking is very difficult. But we are politicians. We all know that democracy lives off change," Merkel said at a joint news conference during Obama's farewell visit to Berlin as President.

Coincidence

The fact that Merkel is sharing the spotlight with Obama and Trump on the same day is a quirk of the calendar: the former president was invited to the Berlin event organized by the German evangelical protestant church a year ago, long before his successor was even elected.

But the presence on European soil of the current and immediate past US President will inevitably draw comparisons about their leadership styles and policies, especially as Obama remains popular in Europe while Trump is not.

There is deep concern in Europe, for instance, about Trump's hostility to anti-climate change policies pursued by Obama, as well as his attempt to institute a ban on travel to the United States of residents of several Muslim nations.

And Obama largely pursued a foreign policy based on multilateralism, which is more to the taste of European leaders, than the "America First" approach that is now the organizing principle of US diplomacy.

Obama's team insisted he was not in Germany to play politics.

"When we agreed to do this, they had not yet set the Trump schedule, we did not in fact know he would be there when we made this decision," said an Obama foundation official, pointing out that the Kirchentag event -- the biennial congress of the German Protestant Church -- had been planned months ahead of time.

Obama also built his schedule to fit in around Merkel's busy diary as a current world leader, and the Thursday date was most convenient for her.

The official stipulated that "is not set up as something where Obama will be asked to respond directly to things that Trump is doing because he has made clear that he doesn't see his role as a former President responding to everything that Trump says or does."

Still, Obama is not beyond oblique references to the turbulent events of the last four months.

"So, what's been going on while I've been gone?" he quipped in the first public appearance of his post presidency in Chicago in April.

And the fact that Obama and Merkel will sit side-by-side on Thursday cannot help but be seen in a political context, especially since the German chancellor is running for a fourth term in office in September's election.

His visit comes shortly after Obama endorsed new French President Emmanuel Macron ahead of the run off in the presidential election this month saying he represented "the values that we care so much about."

Obama had already delivered an endorsement of Merkel's re-election run, albeit in a light-hearted tone, during his visit to Berlin last year.

"I try to make it a rule not to meddle in other people's politics," Obama said, before reeling off a warm tribute of Merkel. "If I were here and I were German, and I had a vote, I might support her. But I don't know whether that hurts or helps."

Clearly, Merkel, who risked her career to accept hundreds of thousands of mainly Muslim refugees pouring across Germany's borders, like Macron, is the kind of leader whose values Obama shares, in a Europe that has recently been rocked by the rise of populist politics that looks much like the outsider strain of anti-establishment politics that Trump rode to victory.

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Obama said last year that Merkel's action on refugees, one that was deeply unpopular among some Germans, put her on "the right side of history."

Trump meanwhile slammed the move.

"I think she made one very catastrophic mistake, and that was taking all of these illegals," Trump said during an interview with the German newspaper Bild and the London Times in January.

Still, despite her affection for Obama, Merkel is nothing if not a realist. And she knows that the future of the Western alliance may rely on her carving out a workable relationship with Trump.

And while the White House may bristle at coverage of Obama's friendship with Merkel, the history of the ex-President and the German Chancellor may contain some good omens for Trump.

After all, it was hardly love at first sight when Merkel first beheld Obama.

In fact, she was affronted by the young rising political star's request to deliver a 2008 campaign speech at the Brandenburg Gate, the iconic spot where Ronald Reagan once beseeched Soviet leader Mikhail Gorbachev to "Tear Down this Wall."

Merkel blocked Obama from using the venue, and he delivered a speech instead to several hundred thousand of young Germans at the Victory Column in mile or so away.

At the time, Obama's soaring rhetorical style appeared to irritate the bookish Merkel.

In an email to then-Secretary of State Hillary Clinton, released by the State Department during disclosures from her private emails server, her friend Sidney Blumenthal passed on observations of a former US ambassador to Berlin John Kornblum.

"He says she (Merkel) dislikes the atmospherics surrounding the Obama phenomenon, that it's contrary to her whole idea of politics and how to conduct oneself in general. She would welcome a more conversational relationship with you," Blumenthal wrote.

And even as respect between Merkel and Obama gradually grew, there were bumps in the road.

Germany for example abstained in a UN Security Council vote before the US-led intervention in Libya -- a move that in retrospect looks prescient given the chaos that unfolded in the country after the toppling of Colonel Moammar Gadhafi.

Then, revelations that the NSA had been listening in on Merkel's cellphone temporarily strained the relationship with Obama -- who stopped the practice after it was revealed by fugitive intelligence contractor Edward Snowden.

But the intellectual approach to governing that both shared brought them back together, as well as the vital nature of the US-Germany relationship.

Now, Merkel, who is expected to win re-election, has the task of starting all over again, with a new US president with whom she has little in common.