That is oversimplified to the point of inaccuracy.
Taiwan is a democracy, and one of the major parties firmly opposes any concept of Chinese rule and seeks recognition of Taiwan. The other party leans towards being the sole leader of all of China. However in practice (being currently elected) they just improve economic ties with China while opposing unification or formal recognition of Taiwan.
The PRC sees Taiwan as a province of China that they should rule, as you mentioned.
Taiwan is a democracy, and one of the major parties firmly opposes any concept of Chinese rule and seeks recognition of Taiwan. The other party leans towards being the sole leader of all of China. However in practice (being currently elected) they just improve economic ties with China while opposing unification or formal recognition of Taiwan.
The PRC sees Taiwan as a province of China that they should rule, as you mentioned.