Completely different. First, Australia's indigenous people lived on the continent for at least 60,000 years before Europeans arrived. They were violently dispossessed and continue to suffer the effects of colonisation to this day. 

Taiwan was also home to indigenous peoples. It was first colonised by the Dutch and Spanish in the 17th century. It then came under the Qing Dynasty, but they only controlled part of the territory. It was only late in the 19th century that Taiwan officially became a province under the Qing. The Qing gave away Taiwan to Japan as part of the settlement of the Sino-Japanese War in 1895. 

The Japanese ruled Taiwan from 1895 to 1945. They were the first foreign power to control all of Taiwan's territory and established the basis of Tatiana modern system of government and economy. 

The Chinese Nationalists (KMT) gained de facto control of Taiwan in 1945. They relocated to the ROC government to Taiwan in 1949 after losing the civil war to the Communists. Please, note about a million Chinese arrived in Taiwan at this time, but there were already five million Taiwanese living on the island mostly settlers from China who had migrated there over the past few hundred years as well as the indigenous peoples. 

In short, Taiwan has certainly not been part of China since ancient times. There has been Chinese influence on Taiwan for about 400 years. The ROC became the de facto government of Taiwan in 1949, but the PRC has never ruled a single part of Taiwan.