Historically, only larger cities had things you might recognize as a postal code. For example: Boston 8, Mass. The current abbreviation for Massachusetts is MA. And some changed - such as NB being Nebraska (and is now New Brunswick) and Nebraska is now NE.
On older letters, you'll see the red abbreviations instead of the more modern ones:
https://en.wikipedia.org/wiki/List_of_U.S._state_and_territo...
And due to historical inertia, very little has changed since the current (5 digit) system was created 60+ years ago.