The moon has a 3d model in the sky that is illuminated by the sun's direction to show accurate phases during gameplay.
Contributed by retrolinkx
The Jet Cola vending machines found in the US and European versions of the game were originally Coca-Cola machines. Sega only acquired the rights to use the brand name in the Japanese release, so the vending machines had to be changed for the others versions.
Contributed by Mr. Kite
In the original Japanese version of Shenmue II, Yuan was a cross-dressing man. However, Sega of Europe did not find this suitable, so they re-recorded his lines with a female Japanese voice actress and swapped his gender.

Additional lines from other characters were also changed from the Japanese release. Dou Nin originally says "What the hell did you do to my cute love thing?", while in the European release this was changed to "What the hell did you do to my partner?"

Yuan's gender change was kept in the English version of the Xbox release.
Contributed by retrolinkx
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Shenmue II was intended to be released on the Dreamcast in North America but it was cancelled and ended up being ported to the Xbox in both North America and Europe. However, the Dreamcast version was released in Japan and Europe.
Contributed by ABOhiccups
In the Dreamcast version, it's possible to transfer save data from original Shenmue to Shenmue II. However, as to be expected, this was not an option in the Xbox release.
Contributed by ABOhiccups