For President Trump, the first day of his visit to Beijing was all about the personal relationship between him and Xi Jinping, the Chinese leader.

“You’re a great leader,” he told his host, whom he has often said he admires for his “powerful” control over a nation of 1.4 billion people. “I say it to everybody.”

Mr. Xi, unsurprisingly, spent little time on flattery. Once the 21-gun salute and precision-marching by units of the People’s Liberation Army were finished, the disciplined Chinese leader plunged right away into setting boundaries for the two country’s relations. The red line was Taiwan, he said, making it abundantly clear that Mr. Trump’s effort at rapprochement could crash on takeoff if he interferes with China’s long-term effort to take control of the self-governing island.

“The U.S. must handle the Taiwan issue with utmost caution,” he said according to a readout from Xinhua, China’s official news agency. The warning came just minutes into his public remarks in the Great Hall of the People, the center of power for the People’s Republic starting just a decade into Mao’s revolution. For Mr. Xi, it was all about setting boundaries, from the start.

The moment seemed to capture the new equilibrium between the two adversaries. Mr. Xi arrived highly scripted, leaving no doubt that for all of China’s problems — deflation, depopulation, the bursting of the real estate bubble — the moment when China acts as a peer superpower had arrived.

At every turn, at least has he began his two-day trip to China, Mr. Trump sounded conciliatory, the exact opposite of his portrayals of China in public appearances back home, where during his presidential campaigns he has talked about the country as a job-stealer and national security threat. Mr. Xi, while smiling and welcoming to Mr. Trump, was quietly more confrontational — especially on Taiwan, where he delivered an unequivocal warning.

The gap spoke directly to the new level of confidence and authority Mr. Xi has adapted in his public speech, despite his challenges with the domestic economy, as he watches the United States plunge into conflict with Iran, another Middle East confrontation with no easy exit.

The Chinese president designed the day meticulously, down to a visit to the Temple of Heaven, the Ming dynasty complex not far from the Forbidden City. As Mr. Trump sat in the 13th-century wonder, he got a history lesson from the Chinese leader, tailored to echo the modern era.

At his toast at a televised State Banquet on Thursday night, Mr. Trump came with a lesson of his own, describing links between China and the United States that went back to the Empress of China, the ship that took a 14-month journey in 1783 to open trade and bring the first American diplomats to what was then known as Canton, now called Guangzhou.

“We’ve gotten along when there were difficulties, we worked it out,” Mr. Trump said. But even then he cast relations in personal terms, making clear that the huge divisions between the two countries had to be solved by two strong leaders.

“I would call you, and you would call me whenever we had a problem, people don’t know, whenever we had a problem,” he said. “We worked that out very quickly, and we’re going to have a fantastic future together.”

For his part, Mr. Xi returned to his mantra: to keep from turning competition into conflict, the two nations must keep from falling into the “Thucydides Trap.”

(The trap, popularized by the Harvard professor Graham Allison in his book “Destined for War: Can America and China Escape the Thucydides’s Trap,” comes when a rising power challenges a status-quo power, often leading to war. “It was the rise of Athens and the fear that rise engendered in Sparta,” the ancient Greek historian Thucydides wrote, “that made war inevitable”.)

Mr. Xi proposed a familiar solution: ban talk of competition between the No. 1 and No. 2 economic superpowers — a regular staple of the Biden White House — and focus on “stability,’’ a governing characteristic rarely associated with Mr. Trump.

“The common interests between China and the United State outweigh our differences,” Mr. Xi said, according to state media. “Stability in China-U.S. relations is a boon to the world.”

But unlike Mr. Trump, he explored the alternative scenario.

“If handled poorly, the two countries will collide or even clash, putting the entire U.S.-China relationship in an extremely dangerous situation,” he said, a clear reference to Taiwan, according to the readout.

If much of this sounds familiar, it was. Mr. Xi has go-to homilies, part of his philosopher-king approach to ruling over China. And in this summit he invented one new one: He said he agreed with Mr. Trump on “a new vision of building a constructive China-US relationship of strategic stability.”

As Rush Doshi, a China scholar at Georgetown University noted, that sounded like an effort “to lock in a ‘truce’ favorable to them, and they want to do so beyond Trump, with this post-trade war détente setting the base line.”

Future disputes over China’s excess manufacturing capacity or rebuilding American military capability in the Indo-Pacific could be declared “a violation of this frame,” he wrote on X.

The contrast with Mr. Trump’s style — where summits are first and foremost for instant “deals,’’ usually ones he can boast will provide jobs or sales — is often jarring. Mr. Trump, for example, brought a group of business executives, whose presence he said was intended to show “respect” for China while seeking market access.

It had a 1990s ring to it, the days when Bill Clinton and George W. Bush brought business leaders to explore the promise of the Chinese market, often for the first time. But Mr. Trump’s delegation came with decades of experience, much of it bitter. Some of them were survivors of the battles over intellectual property theft and sharp restrictions intended to favor local Chinese industry.

Mr. Xi did not bring an equivalent group. There were no executives from BYD, the huge Chinese carmaker trying to figure out how to do business in the United States, or DeepSeek, the innovative artificial intelligence firm at the heart of the battle with A.I. firms in the United States.

There were other discordant notes, heard just beneath the noise of the clinking glasses and optimistic toasts. In contrast to the Chinese readout, the American account, released by the White House, talked about cracking down on fentanyl precursors, a long-running issue with China, and buying American agricultural goods. It did not mention Taiwan, or China’s restrictions on rare earths, or its rapid nuclear weapons buildup.

The White House also described the United States and China as aligned on the need to reopen the Strait of Hormuz, and keep it free of Iranian tolls. All that was true, but ignored the deeper complication: despite American entreaties, China is unlikely to deploy whatever influence it has with the Iranians for free. What the price might be is unclear.

The real test of how these two men debate their differences might come on Friday morning, when Mr. Trump is scheduled for much smaller meetings with Mr. Xi. It is the kind of session he likes best: leader to leader. And once he leaves Chinese airspace, he seems likely to present his preferred version of those talks.

The Chinese government will likely be more circumspect.