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…

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.