(I'm not going to use the hanzi or even proper pinyin for some terms because I only know them from speaking as an absolute beginning learner.)

In Mainland China the currency is the "yuan" but in practice nobody calls it that. Instead they say "kwai".

I've just arrived by ferry in Taiwan from China and here the currency is the "New Taiwan Dollar".

Should I refer to it by the term "yuan", "kwai", or by an adaptation of the English word, something like "dola"?

Bonus: What about when referring to the Old Taiwan Dollar between 1946-49 or the Taiwan Yen during the time under Japanese rule?