I think your referral to 'China' is the mainland, also known as The People's Republic of China. The Republic of China (Taiwan) is part of China as in 1949, they both emerged and called themselves China.
In my opinion, Taiwan is now independent, as they have their own flag which differs from the flag of China and they both have their own individual anthems. And in most cases, they would often call themselves Taiwanese instead of Chinese, and during a world event, their home-region would just be known as Taiwan, not China.
"The opposition Pan-Green Coalition (majority Democratic Progressive Party or DPP) regards Taiwan to be an independent, sovereign state synonymous with the ROC, opposes the notion that Taiwan is part of China, and seeks an eventual declaration of Taiwan independence."
As stated on Wikipedia, PRC and ROC are states, if Taiwan would not be a part of China anymore does that mean PRC and ROC would not be states anymore? Would they just call Taiwan an independent country along with China?
Despite all of that, Taiwan and China are similar in many different ways, both speak the same official dialect which is Mandarin and have similar cultures.
To conclude this, I would say that Taiwan is independent, its classification as a state or a country is still to be verified.
My background is Chinese.