The Chinese word in question, 'sheng', refers to a province of a
nation. The reason why it appears on the license plate of taiwanese
cars is because until ROC changes their constitution on this
matter, Taiwan remains a province of the Republic of China. The
Kuomingtang has always asserted that Taiwan is a part of the ROC,
which includes the rest of Mainland China. The constitution of the
Taiwan has reflected that since the time of Chiang Kai Shek. In
fact, there is an official in the Taiwanese government, Taiwan
'sheng zhang' (literally head of the province), which is distinct
from the position of the President of the ROC, which includes the
communist-held mainland.
The present ruling party is trying to change that but amending the
constitution to make Taiwan independent will bring about an
immediate military response from China and is not supported by the
US either.
The US is a federation of independent states which freely agreed to
be joined to form a nation. Like in Mainand China and Taiwan, cars
registered in each state or province bears the license plate of the
said province/state.
