They're not. Readers native in one version can't read the other, and there are more than handful that got duplicated in multiple forms, so they're just not same, just similar.

You know, obvious presumption underlying Han Unification is that CJK languages must have a continuous dialect continuums, like villagers living in the middle of East China Sea between Shanghai and Nagasaki and Gwangju would speak half-Chinese-Japanese-Korean, and technical distinction only exist because of rivalry or something.

Alas, people don't really erect a house on the surface of an ocean, and CJK languages are each complete isolates with no known shared ancestries, so "it's gotta be all the same" thinking really don't work.

I know it's not very intuitive to think that Chinese and Japanese has ZERO syntactic similarity or mutual intelligibility despite relatively tiny mental shares they occupy, but it's just how things are.

You're making the same mistake: the languages are different, but the script is the same (or trivially derived from the Han script). The Ideographic Research Group was well aware of this, having consisted of native speakers of the languages in question.