ZIP codes are also deceptive lies: ZIP code maps doesn't exist. The Post Office just has a list of addresses which belong to each ZIP code (which essentially means, which post office delivers mail to which address). They provide these lists of address to third-party mapping companies, who draw up maps of what a ZIP code hypothetically looks like based on the set of addresses. The post office, however, is constantly moving addresses between ZIP codes, as they update their postal routes to make them more effective.
To a first approximation, ZIP codes are post offices. My understanding is that sorting starts with the postal codes, but I'm not clear exactly how much sorting happens where. For instance, the first three digits of the post code denotes a regional central processing facility. When 123xx has mail for 456xx, do they sort it before or after sending it to 456xx? Does the central facility for 123xx sort the mail for 12345, or just send it all to the post office? I could see it going either way.