Good question!! I've been asked by many people about this. Well, since i'm not good at history, so I would skip the long story of how mainland china and taiwan split decades ago. In short, after World War II and the civial war in China, there were two Chinas. One communist in mainland(PRC), and the other led by KMT who withdrew from mainland China to Taiwan(ROC). UN was about to acknowledge both Chinas, as the same as north and south Korea. But our president at that time couldn't tolerate the fact that the communist china was recognized too. So we(ROC, Republic of China) left UN and the PRC took over. Since then, whenever china is heard, people think of mainland china. No one thinks of Taiwan, and tend to think Taiwan as a part of China because China claims so. We gradually give up on calling ourselves Chinese, and we call ourselves Taiwanese to avoid confusion.

Your question only applies to Taiwanese, or people who live or origin from Taiwan. It's not suitable for Chinese (people from the mainland, or PRC) since they don't speak Taiwanese. People from the Chinese province, Fujien, speak a similar language though.

Ethnically, yes, my ancestors came from mainland China centuries ago. So that makes me Chinese in that respect. Culturally, we share the traditional chinese inheritage, or we might have even much more since we didn't go through the cultural revolution years ago as the communist china did. So you can call me chinese in that sense. But you don't call me chinese, or I would deny that I'm chinese when it comes to national or political identity, since whenever china is mentioned, it's PRC or mainland china. Taiwan is never governed by China, at least, not the communist china.

But would you call a Singaporean Chinese? No, because he might be Malays or Indians. You might call him Chinese in terms of his ethnic background, right? So I'm a Taiwanese, in terms of my national identity, and I speak Chinese (the language, or Mandarin to be more precise).

Am I making a fuss about all this? Maybe? But if you were in my shoes, you would have known how I feel (or how we feel) and why I would explain like this. But again, my bf often teases me by saying I'm chinese......at moments like that, I can just laugh and complain! :-)