With few exceptions, the word for Tea in a country depends on how it was originally transported there.

See: Tea if by sea, cha if by land: Why the world only has two words for tea

https://qz.com/1176962/map-how-the-word-tea-spread-over-land...

Wow. I had absolutely no idea! Thanks for sharing that link, learned something new today

I thought Chai originally comes from the Chinese word 茶 (Chá).

Correct -- the etymology of all "chai"s and "tea"s can be traced to Chinese:

https://en.wikipedia.org/wiki/Etymology_of_tea