These two countries are pretty different. Treating them as the same country, as you do, is sort of like confusing North Korea with South Korea (e.g., "Korea is a rogue state, and that's why we need to station more troops across the border in Korea so we can fight the Koreans when they invade Korea!!"). You need not get into some sort of big historical discourse, and you can just follow what the US government and the media do. In fact, it seems that calling both countries "China" is what led you to make the erroneous statement about the item in question. China has an economy that can produce vast amounts of cheap goods that are sold globally. Taiwan just doesn't.