I used the word China in other comments because I didn't know what to call it otherwise, hoping that in the context of Taiwan it is clear what I mean
Under no circumstances is Taiwan every seriously referred to as "China," not even "Republic of China," the official name in the constitution, is really used anymore. The passports now prominently say "Taiwan," and polling indicates that "Chinese" identity in Taiwan is dying swiftly with the settler colonialist KMT.
The sibling comment may be referring to political discussions between politicians, especially when talking with PRC officials. I'm not sure, I've almost never heard those terms used except by really weird super-KMT taxi drivers.
The parent comment that "Taiwan calls itself China" is simply incorrect, and the government mentioned, in the 70s, was a KMT totalitarian government that's been essentially overthrown as of the 90s.
It's a pointed issue that you'll often find heated responses from because Taiwan, for basically the first time in its history as a globally participant nation, is finally getting to establish its own identity, separate from the Dutch, the Qing, the Japanese, and the ROC/KMT settler-colonialists. There's great fear that the CPC, having failed to win a culture war here with han chauvinism / han supremacy, will simply resort to violence to imperialise the nation.
對岸 /duì àn/ 'opposite [side of the Taiwan] Strait' is a neutral term coined specifically to avoid the controversy.
If talking about politics, another neutral way could be to just say 北京 /Běijīng/.