Taiwan is actually an state, but China don't recognize it the way we didn't recognize the IS. Of course, Taiwan is in much better situation than the IS, but the underlying logic is the same. A state government don't recognize other states just because they are a state.
The PRC is shrewed in its policy of non-acknowledgement, and we were careless in ours. It is better to acknowledge your allies with names that piss them off, than not acknowledge them with names they like.
