When Kevin Rudd, the former Australian prime minister and longtime China expert, told a German newsmagazine recently that a Cold War between Beijing and Washington was “probable and not just possible,” his remarks rocketed around the White House, where officials have gone to some lengths to squelch such comparisons.

It is true, they concede, that China is emerging as a far broader strategic adversary than the Soviet Union ever was — a technological threat, a military threat, an economic rival. And while President Biden insisted at the United Nations last month that “we are not seeking a new Cold War or a world divided into rigid blocs,” his repeated references this year to a generational struggle between “autocracy and democracy” conjured for some the ideological edge of the 1950s and ’60s.

Yet the question of whether the United States is entering a new Cold War is about more than just finding the right metaphor for this odd turn in superpower politics. Governments that plunge into a Cold War mind-set can exaggerate every conflict, convinced that they are part of a larger struggle. They can miss opportunities for cooperation, as the United States and China did in battling Covid-19, and may yet on the climate.

And the issue of whether this is a Cold War, or something quite different, lurks just beneath the escalating tensions over economic strategy, technological competition and military maneuvers — undersea, in space and in cyberspace.

Without a doubt, the past few weeks have resounded with echoes of old-style Cold War behavior: the Chinese Air Force running sorties inside Taiwan’s air identification zone; Beijing expanding its space program, launching three more astronauts to its space station and accelerating its tests of hypersonic missiles meant to defeat American missile defenses; and the release of a top Huawei executive for two Canadians and two Americans inwhat looked like a prisoner swap. At the same time, the U.S. announced it would provide nuclear submarine technology to Australia, with the prospect that its subs could pop up, undetected, along the Chinese coast. It didn’t escape Chinese commentators that the last time the United States shared that kind of technology was in 1958, when Britain adopted naval reactors as part of the effort to counter Russia’s expanding nuclear arsenals.

And just before the announcement of the Australia deal, satellite photographs revealed new Chinese nuclear missile fields, whose existence Beijing has not explained. American analysts are uncertain about the Chinese government’s intentions, but some inside American intelligence agencies and the Pentagon are wondering whether President Xi Jinping has decided to abandon six decades of a Chinese “minimum deterrent” strategy, even at the risk of setting off a new arms race.

The constant background din of cyberconflict and technology theft was one factor behind the Central Intelligence Agency’s announcement this month that it had created a new China mission center to position the United States, in the words of its director, William J. Burns, to confront “the most important geopolitical threat we face in the 21st century, an increasingly adversarial Chinese government.”

For all this, Mr. Biden’s top aides say that the old Cold War is the wrong way to frame what is happening — and that the use of the term can become a self-fulfilling prophecy. Instead, they argue that it should be possible for the two superpowers to compartmentalize, cooperating on the climate and containing North Korea’s arsenal, even while competing on technology and trade, or jousting for advantage in the South China Sea and around Taiwan.

The White House is loath to put a label on this multilayered approach, which may explain why Mr. Biden has yet to give a speech laying it out in any detail. But his actions so far look increasingly like those in a world of competitive coexistence, a bit edgier than the “peaceful coexistence” that the Soviet leader Nikita S. Khrushchev used to characterize the old Cold War. (Interestingly, after meeting this month in Switzerland with Jake Sullivan, the president’s national security adviser, China’s top diplomat said he objected to any description of the U.S.-China relationship as “competitive.”)

But if the administration is still struggling with the terminology, it says it knows what this isn’t.

“This is nothing like the Cold War, which was primarily a military competition,” one of Mr. Biden’s senior administration advisers said in an interview, speaking on the condition of anonymity because, in the Biden White House, there is no area where words are measured more carefully than in talking about relations with Beijing.

In July, Mr. Biden’s top Asia adviser, Kurt M. Campbell, told the Asia Society that the Cold War comparison “obscures more that it illuminates” and is “in no way helpful, fundamentally, to some of the challenges presented by China.”

The deep links between the two economies — the mutual dependencies on technology, trade and data that leaps the Pacific in milliseconds on American and Chinese-dominated networks — never existed in the more familiar Cold War. The Berlin Wall not only delineated a sharp line between spheres of influence, freedom and authoritarian control, it stopped most communications and trade. The year it fell, 1989, the United States exported $4.3 billion in goods to the Soviets and imported $709 million, an inconsequential blip for both economies. (In current dollars, those numbers would be a bit more than doubled.)

In this superpower standoff, all those lines are blurred, with Huawei and China Telecom equipment running data through NATO nations, the Chinese-owned TikTok app active on tens of millions of American phones, and Beijing worried that the West’s crackdown on selling advanced semiconductors to China could cripple some of its national champions, Huawei included. And yet, even through a pandemic and threats of “decoupling,” the United States exported $124 billion in goods to China last year and imported $434 billion. That made China the largest supplier of goods to the United States, and the third largest consumer of its exports, after Canada and Mexico.

“The size and complexity of the trade relationship is underappreciated,” Mr. Campbell said in July, as part of his argument of why this moment in time differs dramatically from the Cold War of 40 years ago.

But, another of Mr. Biden’s advisers noted the other day, psychology counts for as much in superpower politics as statistics. And whether or not the two countries want to call this a Cold War, they are often behaving, the official noted, as if “we are already immersed in one.”

That is the central argument of those who contend that a new Cold War — one very different from the last — is quickly coming to dominate Washington’s dealings with its central rival. “People think that the only definition of a Cold War is the U.S.-Soviet model,” said Paul Heer, a longtime C.I.A. analyst who spent years focused on Asia, “which it need not be.”

He agrees with the White House officials who say that the new dynamic is not defined largely by a nuclear standoff, or by an ideological struggle in which only one side can prevail. And, he notes in a recent article in The National Interest, the world will not “divide itself into American and Chinese camps.”

But the core element of the old Cold War — “a state of hostility short of armed conflict” in Mr. Heer’s telling — is already clear, as both countries seek power and influence, and to obstruct or contain each other. “There are good reasons that neither government wants to call it a Cold War,” Mr. Heer noted in an interview last week. “But they are both approaching it that way, and the politics on both sides are making it hard to imagine how we will keep it from evolving into that.”

In Washington, one of the few issues that overrides partisan divides in Congress is the specter of Chinese competition, in such crucial areas as semiconductors, artificial intelligence and quantum computing: That is how the “China bill” passed the Senate in a solidly bipartisan vote. (It has yet to come up in the House.)

While few on Capitol Hill want to utter the words, the bill amounts to industrial policy, a once contentious concept in Washington that is now barely debated, thanks to the specter of Chinese competition. For example, the Senate bill, as passed, offers $52 billion to expand domestic chip manufacturing, far beyond anything the United States considered when battling Japan’s technological dominance in the same industry more than 30 years ago. But today Japan’s share of the global chip sales has declined to about 10 percent, and it no longer looms large in American industrial fears.

There are reasons to worry that whatever this era is called, the chance for conflict is now higher than it has ever been. Joseph S. Nye, known best for his writings on the use of “soft power” in geopolitical competition, rejects the Cold War analogy, noting that while many in Washington “talk about a general ‘decoupling’” of the world’s two largest economies, “it is mistaken to think we can decouple our economy completely from China without enormous economic costs.”

But Mr. Nye, who once ran the National Intelligence Council, a group that provides long-term assessments of threats to the United States, warns against the risk of what he calls “sleepwalker syndrome,” which is how the world spiraled into conflict in 1914.

“The fact that the Cold War metaphor is counterproductive as a strategy does not rule out a new Cold War,” he said. “We may get there by accident.”