BUENOS AIRES — When President Trump sits down with President Xi Jinping for dinner here on Saturday, their meeting will be about more than salvaging a cordial personal relationship or trying to contain a trade dispute between the United States and China.

It could foretell whether these two giants — one an established but anxious superpower, the other an ambitious, impatient rising power — are destined to enter a new era of Cold War-like confrontation.

Remarkably, given the stakes involved, the two sides plan no other formal meetings during this gathering of the Group of 20 industrialized nations that begins on Friday. Nor do they appear to have much of an agenda, beyond the trade grievances that Mr. Trump has complained about for months.

That is a testament to how much trade and the personal chemistry between Mr. Trump and Mr. Xi have come to dominate the relations between the United States and China. While these are only subplots in a larger drama that also includes a military contest in the Pacific and nuclear negotiations with North Korea, they could also define the next chapter in that relationship.