Unpublished fares are an entirely different beast. They may be seats that a consolidator purchased and can offer at highly discounted rates. The fare rules could literally contain anything from absolutely no changes allowed to free changes as long as availability exists. They may or may not allow for advance seat selection or the accumulation of frequent flyer miles. If you called an airline looking for the rules to an unpublished fare you would be out of luck. They are not offered for sale by the airline online or over the phone with the airline.
Seat sales launched by airlines are considered published fares as well since (subject to seat availability) such airfares are offered to the public. The rules of such fares are readily available and if there is more than one airline offering the same fare you can count on the rules being virtually the same. A non-refundable fare requiring an advance purchase of 14 days and a minimum Saturday night stay would be just a few of the possible rules of a published fare.
Travel agents often join consortiums which give them purchasing power. The consortium then negotiates rates and amenities with a network of Airlines. Special fares that are sent to select travel agencies - aka consolidator fares. While in some cases, some actually have fare basis codes printed on the ticket, some also do bulk ticketing which do not state the fare. Certain wholesale or group fares, or some fares that are only to be used in conjunction with a travel package (air/hotel/cruise, etc).
Basically the main difference between published and unpublished (or private) fares is that the whole world has access to them (and other carriers), and the latter are only accessible via certain distribution channels.