The world is watching as the leaders of China and the United States meet in San Francisco.

The relationship between the two largest economies is probably the most important state-to-state relationship at the moment. What the two leaders discuss, as well as what they agree on, or disagree on, may determine not only how the two countries treat each other, but even how the world order evolves going forward.

Doubtlessly, the two leaders have much to discuss. Literally everything of significant concern — from the Taiwan question to exports of semiconductors and fentanyl precursor chemicals — may be on the table. Considering Beijing and Washington have presented each other their respective list of grievances in advance, the two leaders will enter discussions with a clear knowledge of what the other side is most concerned about.

But China-US relations have deteriorated to such a degree that expecting too much will only invite disappointment. Not least because Beijing and Washington themselves have seemingly different expectations regarding today's meeting. The US goal is to responsibly manage competition and work together where the countries' interests align, particularly on transnational challenges, and to maintain smooth channels of communication, according to a statement released by White House Press Secretary Karine Jean-Pierre.

Beijing on its part has expressed hopes that the meeting will result in bilateral ties returning to the track of healthy, steady development.

At a routine news briefing on Monday, Chinese Foreign Ministry spokeswoman Mao Ning reiterated Beijing's opposition to the US administration defining US-China relations in terms of competition. The Chinese side has always seen and handled China-US relations in accordance with the principles of mutual respect, peaceful coexistence and win-win cooperation, she said.

Mao highlighted Beijing's wish that Washington will genuinely honor previous promises of not seeking a new Cold War and having no intention of conflict with China, with a clear focus on Taiwan. Stressing "every US administration" has promised to not support "Taiwan independence" — including the current one — she urged Washington to oppose "Taiwan independence" with practical actions.

But despite US Commerce Secretary Gina Raimondo dismissing the notion of a military conflict with Beijing over Taiwan when speaking to CNN, she once again framed relations in terms of "great competition". Such different views going into the talks are symptomatic of the present strained relations, if not the cause and effect.

Given the two sides' divergent framing of relations, the two leaders need to demonstrate that they are genuinely trying to shape common contours for the relationship if the two countries are to act in recognition that they have a shared interest in continuous, constructive engagement and collaborating whenever, wherever possible.

How the two sides define their relations after the meeting will shape their approaches to each other in the foreseeable future.