If you can get your hands on it, I recommend the 4 episode BAFTA-winning mini-series about it: https://en.wikipedia.org/wiki/Mr_Bates_vs_The_Post_Office
A lot of the times both "zipcode" and "state" are mandatory fields.
Zipcode is easy, the platform likely wants my postal code.
You have to be a little bit more creative with state, sometimes "We don't have any states" is fun to see printed on your address label on a parcel, other times "Denmark" could be considered a state in the EU and that can be an answer, but most times "N/A" is enough.
My postal code is 2200 (København N), and that form didn't do anything for me.
All zip codes are postal codes, but not all postal codes are zip codes.
At my last gig, this sentence was said a lot, and people kept confusing the two, both in code and in daily speech, so maybe colloquially they are the same :)