

Taiwan is the island, also known as Formosa, and it is ruled by the Republic of China. Separately, but still part of that state, there’s the autonomous mainland provinces, calling themselves the People’s Republic of China, a rebel faction which somehow steadfastly refuses to declare independence.
Nah West Taiwan is the western half of Taiwan. It’s an island, not a state, just as Denmark is not Jutland, or Spain, or Portugal (fight!) Iberia.