Taiwan (ROC) is a bit of an odd duck because so many places treat them as different but don't do it 'officially' because China demands that they don't as part of maintaining relations with the PRC. For example the US sells them arms after all, it's not like the US completely refuses to admit they exist. Many countries have quasi-embassies in the form of Taipei Economic and Cultural Representative Offices (TECRO) which are definitely totally not embassies just act like them in pretty much every way.

To be fair, the issue here is also that for most of the last 70 or so years the Taiwanese government actually claimed to be the rightful government for ALL of mainland China and even occupied its seat at the UN in that capacity for a time. I don't think anyone argues that Taiwan - outside of the Indigenous population which are a minority - see themselves as anything other than Chinese.