multilingual documents

Question about Chinese and Korean typography

From time to time i had to design documents that are tri lingual, or bi-lingual.
its almost always, spanish, english and another language, the last two were Chinese and Korean...

Usually i receive documents in word, with the text in chinese, and usually i don't have problems opening it. The trouble comes when i import or copy it in Indesign, because most of the times the font used by word is not the same that indesign uses for the same language.

I understand that in the mac there are some system fonts that are there to be used in this cases. For example, for the chinese document I used the MS Mincho, and after looking carefully I understood that the other two fonts (MS PGothic and MS PMincho) are like te times and helvetica versions of this font.