Fares are not the end of the story. There is another unit of representation between a fare component and a complete ticket, called a priceable unit (PU). A priceable unit is a collection of 1 to 4 fare components in one of a small number of fixed geometric shapes. An analogy is that if fares are atoms, priceable units are the molecules used to build complete tickets. It's not entirely correct, but a good working intuition is that a priceable unit is the smallest group of flights and fares that could be sold on their own.
The simplest priceable unit is the one way PU built from one fare component. Others include round trip PUs and circle trip PUs built from 2, 3 or 4 FCs that form a loop. Open jaw PUs are like circle trips with one FC missing; usually the open gap must be shorter than the distance flown in any of the flown FCs.
The airlines use priceable units as a domain in which many fare rules apply. For example, many of the least expensive fares have a Saturday night stay restriction. The airlines often define such a restriction by reference to the priceable unit containing the fare in question: “there must be a Saturday night between the departure of the 1st flight in the 1st FC of the PU and the departure of the 1st flight in the last FC of the PU”. It is common for fares to require that other fares in the same PU be on the same airline.
Importantly, many of the cheapest fares, known as round trip fares (to be distinguished from round trip PUs and round trip journeys) have rules that prohibit their use in one way PUs. That means that for a round trip fare to be used, it must be combined in a priceable unit with at least one other fare; it is round trip fares that usually impose Saturday night stay restrictions. The net effect is that to use a (cheap) round trip fare one must fly a journey with at least two flights separated by a Saturday night, and must use at least two fares to pay for the journey.
As will be discussed, priceable units are responsible for much of the theoretical difficulty in pricing air travel.