It’s between a saga and a series.
A series is when you write a collection of stories that are all connected in one way or the other. This can include stories about one person in particular (think of Twilight—it’s all about Bella and her world) or it can have various perspectives, including companion novels (like for Jenna Moreci’s books where the first is about a guy named Tobias and the second in her series is of someone else, and it takes place the same time as the first book). But it can also have other perspectives and their storylines as long as they intercept the one major timeline and characters, like in the Avengers series.
Sagas, on the other hand, is one major story that takes place in-between multiple stories like Lord of the Rings, and this can include the lives of those characters (being in their perspectives, etc.)
Franchises, however, would refer to the movie world (mostly) but it would deal with everything that is in relation to the original story. So this includes spin-offs, remakes, other parts of the series. So to give an example, Avengers is a franchise. You have the one overall arching story (between the actual Avengers movies) then you have the other parts of the series (like Iron Man, Captain America, all of their sequels), then you have the spin-offs (the animated series, Agents of SHIELD, and now the upcoming show about Loki).