What the other guy said is not exactly correct.

So while they are both China, both claim that the other is the illegitimate government of China. The long of the short is that during the tail end of world war II communist forces rallied and drove out the Japanese from mainland China and Manchuria. They forced the capitalist government forces literally into the ocean and they retreated to Taiwan after they invaded it and took it over from the locals.

They have been a government in exile since the end of world war II. They claim to be the official Chinese government. Basically imagine if instead of a country called China it was Mom and Dad are fighting and dad has been exiled to the shed where he now lives. And Mom kept the kids and still has the house. And because he has full autonomy over his shed, he's able to produce all these fancy little projects that his neighbor down the street. The United States loves to buy from him. In exchange for all those great services, his neighbor down the street has helped him renovate that tiny shed into a nice tiny home.

They're not independent, no country in earth recognizes them as such. China calls it an autonomous region like Tibet or Hong Kong, they're still fully subject to the mainlands laws, but they decide how to tax and what to do with taxes.

There is an independence party in their local Congress, but that's about it. If they use the weapons the US gifted China to declare independence, then yes China will 'invade,' the same way the FBI invaded sovereign citizen's homes in the US.

Taiwan's own constitution states that it is a province of China. The disagreement is, about who are the rightful government of all China. The western media industrial complex always fail to point that bit out.

Another thing they would rather you didn't know is that Taiwan also claims the same territorial waters in the South China Sea, the same nine dash line, that the rest of China claims.