I tend to think of anything going on since WWI as more of a current event than an historic occurrence, but this is something I've pondered for a while now. During the time in which communist China was not recognised, what was it seen as? A renegade state of Taiwan? A separate entity? And why was such a comparatively small island seen as true China rather than the landmass with, at the time, close to a billion people?
Both regimes claimed the territory held by the other as their own, so those who recognised Taipei considered the mainland part of its territory, only under other management for the time being.
The situation was a legacy of the end of the 1946-49 civil war, when the Guomindang regime was routed on the mainland, retreating with half a million Chinese troops to the island that had been restored to China at the end of WW2 after half a century of Japanese rule.
After some minor confrontations, US-Chinese confrontation in Korea seems to have sealed non-recognition. In May 1951 Assistant Undersecretary of State Rusk declared:
We do not recognize the authorities in Peiping for what they pretend to be. The Peiping [Beijing] regime may be a colonial Russian government - a Slavic Manchukuo on a larger scale. It is not the government of China. It does not pass the first test. It is not Chinese.
The policy found some very odd justifications: at one point it was defended on the grounds that Taiwan had never been restored formally to China by treaty, so remained a distinct territory - oddly as its government styled itself the Republic of China and claimed both sides of the strait.
Odder still in some ways were the 1970s, as US presidents visited Beijing, US diplomats sat alongside their mainland counterparts at the UN and Taiwan retained the sole US Embassy.
Peculiarities persist. At present Beijing doesn't mind Taipei quietly claiming the whole mainland, but threatens action if it ever relinquishes its claim to PRC-held territory by declaring independence.