Are a lot of Taiwanese actually the same people as Singapore origin wise since you come from Fujian and even speak Hokkien? Or is that exaggerated?
Only partially yes. A plurality (not majority) of Singapore Chinese are from Southern Fujian and there is a cultural connection which makes Singaporeans more favourable to Taiwanese. But during WW2 the Singapore Fujian community was anti-Japanese and pro-CCP, as represented by their primary leader
. The Taiwan Fujian community who lived under Japanese colonial rule were granted with local authority, given education etc. which made them totally different from all other Chinese because they still don't understand what was bad about Japan.
they still came from China either way so they are no different than the ones that came with the KMT.
Every group who moved out of Mainland China retains the memory of China from that time period. In Vietnam, the Ming descendants 明香 and Qing era immigrants 清人 are considered totally separate; the first left for patriotic reasons and the second for economic reasons and accepted the pigtail, so the former looked down on the latter. In Taiwan it is even worse because very few had a clear understanding of Chinese national identity before 1895 apart from some vague concept of Mandate of Heaven, and their main loyalty was to their ancestral village. The KMT supporters, who just gone through 40 years of revolution, civil wars and invasion, had a very different mentality which focused on national unity.
We have to be alert to this difference because almost all groups who migrated out of China before 1919 have trouble understanding Chinese national identity.