A common question that visitors may ask when visiting Taiwan is "if Taiwan is Taiwan, and China is China, then why do license plates say 臺灣省"?
This question is actually very easy to answer!
When the ROC government moved to Taiwan in 1949, it attempted to retain as much of its governmental structure as possible, continuing to manage each province as an independent unit under the national government. Since the intention was to return to the mainland, "Taiwan Province" was still in actuality Taiwan Province, albeit with its government function reduced significantly as Taiwan Province was the only province the ROC had control over (with the exception of Kinmen and Matsu which are technically in Fujian Province).
So, yes, the license plates do say "Taiwan Province", but that only means Taiwan Province of the Republic of China, not Taiwan Province of the PRC.