In the case of China (and I'm sure someone like /u/keyilan can drop more science on this), the "elements" really aren't that similar at all - even calling them "elements" is an artifact of translating a Chinese concept into a word that's familiar from the Greeks.

The main thing is that there are five of them - wu xing (五行), five movements. They're referred to in the Mahuangdi Silk Texts, so at least going back to the Han Dynasty, a century and a half BCE.

Unlike the four elements, which are sort of foundational essences of stuff (like, Thales: "everything is made of water" vs. Heraclitus: "everything is made of fire"), the wu xing all give rise to each other in one cycle of relations and unmake or destroy each other in another.

Wood (conceptually, "growingness") feeds Fire which burns things to Earth (think:ash) which condenses to Metal (like ice, "condensedness") which melts to Water, which feeds Wood. In the destructive cycle, Wood separates/sends roots into Earth, Earth muddies Water, Water extinguishes Fire, Fire melts Metal, and Metal cuts (or ice kills) Wood.

There's no Air at all in this schema, and I don't believe there are any relationships between the classical elements that have the same one-becomes-another dynamic (aside from some alchemical combinations, which are a different kind of thing).

There are correspondences of a similar kind, though - with cardinal directions ("the middle" being an important direction in Zhongguo, the "middle kingdom"), and with areas of the sky or astronomical phenomena (the wu xing are linked to the five visible planets: Venus, Mars, Jupiter, Saturn, and Mercury) .

I'm not sure just how far back those correspondences go - the oldest wu xing references I know of are allusions in the Yijing (so, metaphysics) and things to do with medicine.

If you want table after table of potential correspondences, Wikipedia's wu xing article has scads of them, some of them even sourced!