One ticketing carrier, city pair and fare basis code contains one set of fare rules (advance purchase, minimum stay, etc.)

The fare rules for one ticketing carrier, city pair and fare basis code can change over time, but at the moment you purchase a ticket, there is only one set of fare rules.

It is important to note that it is the ticketing carrier, not the operating carrier, that (along with city pair and fare basis code) points to a set of fare rules. For example, UA and US could have wildly different fare rules for the same itinerary using the same physical flights. Same with NW/CO/DL.

One of the attributes of the fare rules is the booking class. The purpose of a booking class is 1) the cabin in which you are confirmed (coach, First, etc.) and 2) availability. In order to buy a ticket, you need availability in the booking class along with meeting the advance purchase requirements, minimum stay, day/time restrictions, and so on.