There can be no doubt that the Island
we know today as Taiwan
https://taiwantoday.tw/news.php?unit=20,29,35,45&post=25821
is officially known as The Republic of China.
It is the last bastion of the chinese nationalist party which lost political control of the mainland to Mao's red forces who now run the mainland collectively known as The People's Republic of China.
Despite being relegated to a small island, Taiwan's kuomintang still hopes to recover their lost mainland... thus the bitter dispute of the two Chinas each seeing themselves as the righful heir to a unified china.
Taiwan's RoC is now largely administered by taiwanese island born Chinese.
Then there are of course the taiwanese tribal peoples who are the island's original native lnhabitants and quite culturally distinct from the chinese.
So yeah, i understand the confusion, not all Taiwanese are of a 100% Chinese msinland descend even though they may understand and to some extend look and speak the Chinese language. Perhsps its kinda the island of Okinawa in relation to the Japanese situation