It's like... Ukrainian: чай Russian: чай Belarusian: чай Czech: čaj Slovak: čaj Bulgarian: чай Serbian: чаj Croatian: čaj Bosnian: čaj Makedonian: чай Polish: … Czech: Polish nO. Czech: YOU DON'T-- Polish: HERBATA! All the family: oh, the little rebel!
Meanwhile in Belarusian is still two variants for tea: чай (czaj) and гарбата (harbata).
So is czaj(which is a word in Polish, BTW, but only used in prison slang these days) and funnily enough, both are from Chinese, only the czaj version also passed through Persian. ;)
Based on which word is used for Tea, you can easily identify how given nation came in contact with Tea first – in case of other Slavic nations it's through Turkey and/or Middle East, while Poland first came in contact with it from Dutch East India Company trade, like most of the northern Europe.
There is a pretty good article about it on Wikipedia.
"h" and "ch" are the same sound, it's a matter of orthography. If you wrote "cherbata" you would look like an uneducated Polish person. Luckily it seems that learners almost don't make orthographic mistakes because they learn the writing anyway :D
P.S. Actually, people living near the Eastern or Southern border may pronounce them a bit differently, true. "h" would be more voiced then. But it's regional.