This question, along with “are Taiwanese people Chinese?”, is easy to ask, but takes a while to answer. Taiwan is an country of mostly immigrants. The original inhabitants of Formosa island today only accounts for less than 3% of the population. Similar to the United States, where while everyone is an American, most people can trace their ancestry to somewhere else. Here we use the word Taiwanese as a term for the nationality, i.e. people born and live in Taiwan and/or Taiwanese citizens. Much like trying to explain Taiwan’s political status, answering the question requires one to understand Taiwan’s history of immigration and population composition.
The Han people in Taiwan are very much the same Han people that make up ~92% of China’s population, ~76% of Singapore’s population, 23% of Malaysia’s population, and 18% of global population. In other words, the majority ethnic group in Taiwan is the same as the one in China. Consequently, the same traditional holidays (Lunar New Year, Dragon Boat Festival, Mid-Autumn Festival, etc.) are celebrated in both places, while much of traditional Han Chinese culture is alive and well in Taiwan.
When the Hoklos and Hakkas first started immigrating to Taiwan in the 17th- and 18th-centuries, all of them still identified themselves as subjects of the Ming and subsequent Qing dynasties, i.e. the imperial China. They considered the indigenous peoples as barbarians, and sought to assimilate those they could, but mostly occupied indigenous lands. Like the indigenous peoples around the world, Han immigrants were viewed as invaders by the different indigenous tribes, both in the plains and mountains. After the defeat of the Dutch by Koxinga in 1662, Taiwan (at least the parts occupied by Han people) was controlled by Chinese regimes for more than 200 years (1662-1683 by Koxinga and families, 1684-1895 by the Qing Empire).
When Taiwan was ceded to Japan in 1895, resistance among Han people to Japanese rule was high, as most of them very much still considered themselves subjects of the Qing Empire. For the first 20 years as a Japanese colony, non-Japanese people in Taiwan were treated as less than Japanese people, and the all-powerful colonial government at the time mainly sought to exploit Taiwan’s rich natural resources and cheap labor.
As the Japanese Empire began to expand its ambitions further into other parts of Asia and became involved in the two world wars, its strategy in Taiwan changed. Then-governor general of Taiwan, Den Kenjirō, pursued a policy of assimilation, aimed to turn non-Japanese people living in Taiwan into Japanese subjects. The policy was formally announced in 1919, and within the next 20 years, people in Taiwan were encouraged to speak Japanese, celebrate Japanese holidays, and practice Japanese customs. At the same time, much effort was made to modernize Taiwan, both to construct it as an extension of the Japanese islands and to prepare it as a base for Japanese military aggression. Local social movements also spurred to fight for Taiwanese representation in the Japanese parliament as well as local elected assemblies.
When the Second Sino-Japanese War erupted in 1937, the civilian-controlled Colonial Government was turned over to military control, and the Colonial Government devoted its full efforts to the “Kōminka movement 皇民化運動”, aimed at fully Japanizing Taiwanese society. As a result of this movement, many Taiwanese youths served (voluntarily or drafted) in the Japanese armed forces and were killed during the war. Many people born in Taiwan at the time grew up speaking Japanese in school and sometimes even at home (this is the reason why many older people in Taiwan today still understand Japanese).
In 1945, after Japan was defeated in WWII, the Republic of China, under control of the Chinese Nationalist Kuomintang (KMT), took over Taiwan. Taiwanese people’s enthusiasm towards the mainland government quickly diminished when it became apparent that the KMT was corrupt, hostile towards Taiwanese people, and much less advanced compared to the Japanese colonists.
Of course, the KMT regime understood this, especially after it lost mainland China to the Communists in 1949 and sought to use Taiwan as a base one day to reclaim control of mainland China. Chiang Kai-shek and his son Chiang Ching-kuo, who was president after his father died, pursued a policy of sinicization, and were adamant that the populace understands that Taiwan and mainland are both a part of one China. Under this policy, only Chinese history and geography were taught in schools. Students were required to speak Mandarin, and would be punished for speaking their native dialects of Hokkien, Hakka, not to mention any of the indigenous languages. Everyone was taught to be a patriotic, nationalistic “Chinese”, so that when the “liberation” of mainland occurs, they could provide salvation to the “blood compatriots” across the Taiwan Strait.
It was only after 1988, when Lee Tung-hui and Chen Shui-bian became presidents, did Taiwanese history and geography became a part of the curriculum. For millennials who grew up in Taiwan, we have always learned about Taiwan as a place with its own history and diverse groups of people. Its path crossed with China, but that’s not the whole picture. Sure we still learned about China, but we do so in order to understand the cultural and historical heritage the majority of people in Taiwan have, and at the same time to see how elements from different groups influence one another.
The reason we see more and more people identifying themselves as just Taiwanese, and that the majority of the population either identify themselves as Taiwanese or Taiwanese and Chinese is because just identifying as Chinese is no longer enough. Saying that we are Chinese, which actually covers a plethora of terms with different meanings in the Chinese language, is almost equivalent to saying that we are citizens of the People’s Republic of China, or that we live in China, neither of which are true. We have never felt a connection to the PRC, and while people over the age of 60 may still feel a connection to the ROC and the mainland, maybe because they fought against the Communists and have relatives in the mainland, or because they held a deep belief about a potential reunification of the two sides, those sentiments are very rare among the younger generations.
The PRC likes to say that Taiwan is an “inalienable part of China” since ancient times, and that (re-)unification is inevitable. Among the usual rhetoric, they also like iterate that “the Taiwan compatriots share blood ties with us and there is no force that can separate us.” The rising Taiwanese identity is something the PRC has failed to completely grasp (or perhaps simply pretended doesn’t exist), as it is often regarded as something spurred by “pro-Taiwan independence forces.” It is apparently incomprehensible to the PRC how a group of people with roots that could be traced to China not consider themselves Chinese. From the PRC perspective, it is perhaps simpler to consider its entire population as a homogeneous group, but that is no longer the perspective Taiwan follows. More is being done to re-discover and promote the multi-ethnic identity of Taiwanese people, and Beijing will have to consider that if it is to invade and occupy Taiwan by force, it would face a populace that has a very different idea about their identity.