"Strategic ambiguity" has been U.S. policy toward Taiwan for forty years.
China has said that, if Taiwan declares independence, they will invade.
So Taiwan has kept on functioning like an independent country,
without formally declaring their independence.
Every country knows that Taiwan really is independent, but they're all pretending that it isn't.
Taiwan has never been inhabited by Chinese people.
It has always been inhabited by ethnic Taiwanese.
China conquered Taiwan in the 1700s, but never sent Chinese settlers to occupy it.
In 1895, Japan seized Taiwan. It was returned to China in 1945.
In 1949, the Communists took over China.
The government fled to Taiwan, and took the navy with them.
That's why the Communists didn't seize Taiwan then. They couldn't get there!