Very often ZIP code is used as alias for postal code even in international context. I see "zip code" more often than "postal code" on international address forms.
Can you show me an example of an address form for non-US-based organization that exclusively uses the term "zip code"?
I'm not saying they don't exist, but I'm not sure I've ever seen one.
The US-based organizations using the term "zip code" for non-US addresses are doing so either out of ignorance or expediency, since fitting "zip/postal code" into a space is sometimes not possible.
I've seen it quite a bit in especially older e-commerce software, presumably developed for US use, then "internationalized" as a bit of an afterthought. I also think that many non-native-english-speakers assume zip code is the appropriate translation of postal code since it features rather prominently in (exported) US pop culture.
That doesn't make it correct, and I don't believe that some peoples unequivocally wrong usage of a term should oblige other people to qualify their correct and unambiguous usage of it.
