Originally Posted by
YuropFlyer
Since 1949, last time I checked..
The fact that the PRC does not have direct control over the island does not mean it's not (officially) part of the PRC. Taiwan even does "send" some people to the national congress (in whatever sense you want to see it), don't forget that

There is a reason it says "HK, Macao, Taiwan AND International Departures/Arrivals at PRC airports

Whatever the status of Taiwan/ROC, and regardless of whom you ask (Chinese, Taiwanese, US, etc), for visa purposes quite clearly China recognizes it as an "international" destination outside its jurisdiction for purposes of visas and travel.
I asked about Hong Kong (really just for stronger confirmation) because there is really no dispute that it is part of China, but China has designated it as a special administrative region, and arguably traveling there is not going to another country, even though it has its own visa/immigration standards. As confirmed, it, too, is a different country for TWOV purposes.