The differences between Mainland China (People repbublic of China PBOC) and Taiwan (Republic of China ROC) is an unfinished civil war. Officially the war is still on-going since no cease fire has been agreed by both side.
Mainland China(PBOC) want Taiwan(ROC) back is similar to how West Germany unified East Germany, North Korea want to unified South Korea, and US Union states want the Confederate states back in their civil war.
PBOC offer a peaceful reunification method similar to
one country two systems that was offered to Hong Kong.
Excerpt from ->
https://www.fmprc.gov.cn/mfa_eng/ziliao_665539/3602_665543/3604_665547/t18027.shtml
The Chinese government advanced the proposal of peaceful reunification back in the 1950s. In May, 1955, Premier Zhou Enlai stated that "the Chinese people are willing, when conditions permit, to strive to liberate Taiwan by peaceful means." In May, 1960, Chairman Mao said that provided Taiwan is returned to the motherland, with the exception of foreign affairs which must be handled by the national authorities, all the military and political power and the power of appointing officials may be delegated to the Taiwan authorities. This is the origin of the concept of "one country, two systems". In January, 1979, Deng Xiaoping advanced the concept of "one country, two systems" and stated that "so long as Taiwan returns to the embrace of the motherland, we will respect the realities and the existing system there." On September 30, 1981, Ye Jianying, Chairman of the Standing Committee of China's National People's Congress, officially put forward a nine-point proposal for bringing about the peaceful reunification of the mainland and Taiwan. He said that "after China is reunified, Taiwan may become a special administrative region. It may enjoy a high degree of autonomy and may keep its military forces. The national government will not intervene in the local affairs of Taiwan." "Taiwan's current social and economic systems will remain unchanged, its way of life will not change, and its economic and cultural ties with foreign countries will not change.' A provision on setting up special administrative region was added to the Constitution of the People's Republic of China passed at the Fifth Session of the National People's Congress in 1982, providing legal basis for accomplishing "one country, two systems". On January 30, 1995, President Jiang Zemin delivered an important speech entitled Continue to Strive to Complete the Grand Cause of China's Reunification. In the speech, he elaborated the concept of "one country, two systems" and made an eight-point proposal for improving the across strait relations during the current stage and accelerating the process of China's peaceful reunification.
The details is obviously up to negotiation between the two sides. Currently that negotiation would not happen anytime soon because Taiwan currently has a pro-independence party running the gov't.
Mainland China has also make it clear its position that Taiwan island is a part of China and separating it from China is absolutely unacceptable to China, China would not rule out the use of military force to defend its sovereignty.
According to poll, majority of Taiwanese prefer the status quo. There is no similar poll on the Mainland, although there seem to be an increasing call on Chinese social media for a forceful reunification, but this is likely just a tiny vocal minority.
I think war across the Taiwan strait is very unlikely because there is no real urgency and it is really not in China national advantage. BUT if China sovereignty is challenged or provoked like if Taiwan declared independence then I don't think China leadership would have any other choice.
