China is officially called the People's Republic of China (PRC).
Taiwan is alternatively known as the Republic of China (ROC).
The PRC considers Taiwan to be its 23rd province and claims to have sovereignty over it. Conversely, the ROC claims to have sovereignty over all of mainland China.
Most countries do not officially recognize Taiwan as an independent country, due to China's insistence that nations cannot have official relations with both China and Taiwan. Recommended reading: