no, Taiwan (Republic of China) isn’t China (People’s Republic of China) !
Formosa is the Spanish name of the Island, that was Dutch, Spanish, Chinese and Japanese
in fact Taiwan has been defending her independence since 1945 despite the claims of the PROC.
I have many Taiwanese friends, they think they are independent, have their, flag, government and their army defending them from China. When they speak of themselves they use the term Taiwan and Taiwanese and when they go to China they clearly go to another country.
That is indeed a widespread sentiment in Taiwan (I have spent time in both of them, and they feel like different countries), but if you are still in inclined to think that Taiwan is independent, assert the proposition to a Chinese diplomat. A tip: after you have made your statement, stand back.