The islands are Chinese. The US back Taiwan as an anti-communist and anti-China (divide and conquer) tactic, including because its location. If the communists had lost the civil war, the mainland and Taiwan would all have remained under ROC control and it would have been interesting to see what the US would have come up with, instead (academic and thought experiment but interesting to imagine nonetheless).
In Ukraine the US don't want to be dragged in a war against Russia and things have played well for them so far (really the US are the only winners so far).