WASHINGTON — When President Trump meets President Xi Jinping of China this week to discuss contentious trade issues, they will face each other in another nation that was once the United States’ main commercial rival, seen as a threat to American dominance.

But the competition between the United States and Japan, which hosts the Group of 20 summit this week for the first time, settled into a normal struggle among businesses after waves of American anxiety in the 1980s. Japan hit a decade of stagnation, and in 2010, China overtook it as the world’s second-largest economy.

There is no sign, though, that the rivalry between the United States and China will reach the same kind of equilibrium. For one thing, Japan is a democracy that has a military alliance with the United States, while China is an authoritarian nation that most likely seeks to displace American military dominance of the western Pacific. In China’s competition with the United States, a rancorous trade war has persisted for a year, and issues of national security are bleeding by the week into economic ones. Some senior American officials are pushing for “decoupling” the two economies.

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The main elements in relations — economic and commercial ties — have become unmoored, and few agree on the future contours of the relationship or the magnitude of the conflicts.