Taiwan and Ukraine: Two crises, 5,000 miles apart, are linked in complex ways.

Hours before Russia began its invasion of Ukraine in late February, the Chinese Foreign Ministry issued a statement that was clear, stern and not really about Russia or Ukraine at all.

“Taiwan is not Ukraine,” Hua Chunying, the ministry’s spokeswoman, told reporters in Beijing. “Taiwan has always been an inalienable part of China. This is an indisputable legal and historical fact.”

But with no end in sight to the bloody war in Ukraine and with tensions significantly rising in the Taiwan Strait, the two geopolitical challenges are intersecting in complex and unpredictable ways.

Russia’s foreign minister, Sergey V. Lavrov, on Wednesday wasted no time in linking the two, saying that Speaker Nancy Pelosi’s visit this week to Taiwan was a “manifestation of the same course” that the United States has taken in Ukraine. Even though it was Russia that invaded Ukraine, he blamed the West for the conflict.

The fear since the outset of the war in Ukraine has been that Moscow and Beijing will be driven closer together as the United States casts both issues as a struggle between authoritarianism and democracy — as Ms. Pelosi did in the spring during her visit to Ukraine and on Wednesday while in Taipei, Taiwan’s capital.

There are a multitude of differences between Ukraine and Taiwan, including history and geography. But both embattled democracies sit next to much larger, nuclear-armed military powers ruled by authoritarian leaders who have made it clear that they do not see their neighbors as sovereign states.

One major difference, of course, is that the United States and its allies support an independent Ukraine, but America’s “One China” policy does not support Taiwan’s independence, while remaining purposely unclear about whether Washington would defend Taiwan if Beijing attacks it.

As the nervousness, rhetoric and military posturing surrounding Ms. Pelosi’s visit to Taiwan demonstrated, many are asking what path China will choose, and when.

The White House urged Ms. Pelosi not to visit Taiwan, reflecting Washington’s delicate balancing act as it plays a central role in both dramas, seeking to strengthen the international order around Western values while avoiding a wider conflagration.

While Washington has now offered Ukraine more than $8 billion in direct military support — part of more than $54 billion in assistance that has proved a vital lifeline to Kyiv — President Biden has repeatedly said that he does not want to take any action that could set off a direct confrontation with Russia. So far, despite the mutual bluster, Moscow has been careful not to draw NATO into its war.

The Biden administration has also worked to help maintain solidarity with and among European allies.

But a conflict with China over Taiwan would most likely divide the United States’ allies, especially in Europe.

“No one knows at this stage what the outcome of the Ukrainian conflict will be, but relations between Europe and Russia will never be the same again,” Philippe Le Corre, a French scholar of China and a senior fellow at Harvard’s Kennedy School, wrote in the Ouest-France newspaper. “With Asia, the remoteness — reinforced by the absence of human contact and international travel for two years — does not favor a possible European involvement in a conflict in Taiwan or in the China Sea.”

And while China has offered rhetorical support for Moscow, it has avoided becoming directly embroiled in the conflict. Beijing has not offered the Kremlin military assistance, and it has been careful not to visibly undermine Western sanctions.

Both Russia and China are united in opposing what they consider American hegemony and assertion of global leadership. But China, mindful that it is not ready for a major war and needs open global trade, has always been careful not to push its confrontation with Washington or its allies in the Pacific too far.

“I don’t think that provoking the U.S. over the Ukraine issue would be a response they would take,” said Steven Goldstein, an associate at the Fairbank Center for Chinese Studies and the director of the Taiwan Studies Workshop at Harvard University. “When China gets angry with the U.S. over Taiwan, they punish Taiwan.”

“The biggest danger,” he said in an interview, “is we stumble into something.”

The deeper the United States and China spiral into a cycle of provocation, the greater the chances for a false move that could turn an abstract threat into war.