I'm looking for a word for transliterations that have gone on to become native words apart from their origins. For example, zombie, sarong, besuboru, Kalikimaka. The meanings may differ from the origin word and the pronunciation and spelling may be very different from that in the source language.
Sometimes the terms "loanword" and "borrowing" are reserved for words like this that have become well-integrated into the recipient language and are no longer considered foreign, while ones that haven't been integrated are mere "foreign words". For example, many English style guides recommend italicizing foreign words, but not loanwords; very few authors would italicize "café", since it's thoroughly integrated into English by now.
A transliteration is where you convert అలాగా into alāgā (Telugu to Latin) – it involves changing the script, and is only about writing. Words like Kalikimaka are "borrowings" from one language to another, adapted to satisfy the requirements of the particular language – they are at least in origin an attempt to say "Christmas", "baseball" in Hawaiian and Japanese, in light of the rules of pronunciation of Hawaiian and Japanese. We would say that these are "loanwords". The contemporary English usage of sarong is rather different from the Malay / Indonesian word, so meanings can change (I think the contemporay version of "sarong" is only a few decades old, but it has been in English for longer than that). We assume that "zombie" comes from an African language, but it has been in English for 200 years and the exact path of borrowing is really not known.