Prequel
A prequel is a film that is set before the original film.
Sequel
The most popular type of follow-up there is, a sequel picks up after the original/previous film. Whether that means directly after the previous film’s events, or 10 years after makes no difference – as long as it follows up directly, without any other project being in the way.
Midquel
Also called an interquel, a midquel is… well, something in the middle. Taken within a franchise, it’s the latest entry, but acts as a sequel to one or more of the original films, and in the same time acts as a prequel to others. Otherwise, it can also take place inside a single film – that for instance features a long time skip that is not explored as part of the original project, but the midquel comes back and explores it instead. Examples include Alien vs Predator, Terminator Salvation, Red Dragon, Solo: A Star Wars Story, and The Scorpion King.
so an interquel occurs between two already-established stories. If "Story Z" follows "Story X," but there is room between the two for another story, you could add "Story Y" as an interquel. An example of this in mainstream media would be Black Widow because this story takes place after the events of Captain America: Civil War and before the events of Avengers: Infinity War even though Avengers: Infinity War had already been released by this time.
Inquel
An inquel is a story that takes place within a gap of time in another story. If Story X has a period of time that is rushed through without being fully explored, that would give an author the opportunity to later go back and write an inquel. These are not common, but an example of this would be Bambi II, which occurs during the established events of Bambi. It explores the time period when Bambi is still a fawn and his mother has just died. It ends prior to the time when Bambi is shown as an adult in the first movie.
trequel
A work following a sequel; the third in a series, particularly of films. synonym ▲
Synonym: threequel
Paraquel
A paraquel isn't something you come across very often, but this is a story that occurs within the same world at the same time as another story. This means you will likely see overlapping characters and scenes, though they probably won't all be the same. If an author writes a story of the same events from another character's perspective, that would be a paraquel. If "Story X" and "Story Y" are happening at the same time to two different characters within the same world, the two stories would then be paraquels of each other. My book, The Heart of Everton Inn, is a paraquel in relation to The Secret of Drulea Cottage because the two stories are taking place at the same time, but The Heart of Everton Inn features Adaira Stubbins as the main character, whereas Briony Fairborn is the protagonist of The Secret of Drulea Cottage.
Circumquel
This type of story has events occurring before "Story X" and events occurring after "Story X." I can't recall ever watching a movie or reading a book with this type of story, and it seems like it would be very difficult to create a compelling one. I would think that making two separate stories (a prequel and a sequel) would be a better stylistic choice than putting both past and future events into one story.
postquel (Blend of post- + sequel.)
(narratology) A work of fiction which is set after the events of an earlier installment in a series but is not an immediate sequel.
C.S. Lewis's The Lion, the Witch and the Wardrobe was followed by four sequels beginning with Prince Caspian, but also an inquel (The Horse and His Boy) and a prequel (The Magician's Nephew)