It is true to some extent. While 青 and 靑 have different codepoints, there are plenty of characters of the same codepoint that are rendered differently depends on the language specificed:

https://en.wikipedia.org/wiki/Han_unification#Examples_of_la...

Han characters that are traditionally viewed as variants of one another, or that are simplified from more complex logograms (such as 龜, which was simplified into 亀 in Japan and 龟 in mainland China) tend to have different codepoints, but the stylistically different ones usually belong to the same codepoint.