What's the most detailed level of location can I get only by knowing the ZIP code?

I am looking at APIs to get location information from ZIP codes. So far the most detailed level of location I could get was Country --> State --> City.

Does ZIP code also map to neighborhood / districts ?

I have seen some APIs that return lng lat coordinates for zip code, I guess I could geo-code the coord to find out the more specific area, but I don't know how fine grained it is