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.