I'm curious but what is the distinction between China and Taiwan, I know that Taiwan split off from China, but I don't believe that was very long ago so there really shouldn't be any ethnic difference, I know that this is a pretty sensitive topic for some Taiwanese folk, when they get mixed up, or especially when they use China's version of their flag. Or maybe thinking on this a little more China just claimed the island of Taiwan as part of China so they were considered "Chinese" but ethnically have not much to do with each other?
In very rough terms:
After the Qing Dynasty fell and during and after WW2, there was a long term power struggle over control of China by two factions: The Republic of China (led by the Kuomingtang Party) and the Communist Party.
The Kuomingtang Party initially had a heavy advantage, and was supported by US arms deals and training. The Kuomingtang party, led by Chiang Kai-Shek, also represented China abroad in international diplomatic relations. For example, at the United Nations, they held China's seat (and not the Communists).
However, over time the tides turned, and the Communists eventually prevailed over the Kuomingtang over the mainland China. At the last moment, however, the Kuomingtang Party and Chiang Kai-Shek - along with millions of Kuomingtang supporters and affiliates - fled to the nearby island of Taiwan. From there, the Kuomingtang re-established Taipei as their new capital and continued to represent the Republic of China.
The Communists consolidated control of the mainland China and formed the People's Republic of China.
So now, you effectively have two Chinas - one is called the Republic of China (based in Taiwan) led by the KMT party and the other is the People's Republic of China led by the Communist Party. Both claim to be the "legitimate" China.
A funny detail is even after the Communists won like 99% of China's land, the Republic of China (based only in Taiwan) continued to represent ALL OF China at the United Nations for like 20 more years until 1978 when the Republic of China finally got ousted in favor of the People's Republic China. Since 1978, the government in Taiwan and its 25 million citizens have no representation at the UN.
The PRC uses their economic and military might to pressure every other nation into refusing to recognize the ROC as a legitimate sovereign nation to this day.
Since the ROC actually prexists the PRC, one could argue that it's not so much that Taiwan split from China, but almost rather the other way around. Technically, the current government in Beijing started out as the splitting rebel faction that kicked out the former dominant government. It's kind of like if during the US Civil War, the United States got defeated by the Confederate States - but at the last moment, the US quickly evacuates to Hawaii and continues their governance there, leaving the rest of the continent to the CSA.