An interquel is a game whose plot is set between the events of two previously-released entries in a series. These can be two other games, or any other media like films, books, or comics. The purpose of an interquel is to bridge a gap or fill in details in the timeline relative to the games set before and after it, though it is more often used by developers who are hesitant to extend the storyline past a certain point in the timeline, as seen in the Metroid and Halo franchises. An example of a proper interquel is Metroid: Other M, a 2010 release that is chronologically set between the games Super Metroid and Metroid Fusion.
An interquel should not be confused a midquel, which covers events that predominantly occur concurrently with the events of a previous game. Many midquels are also side story or "gaiden" titles. Examples of this include Half-Life: Blue Shift and Half-Life: Opposing Force, both of which were set simultaneously with the events of the original Half-Life, or Halo 3: ODST, which takes place in the same time period as the second half of Halo 2.
Some games that are interquels may also be side stories. One such example that covers ground in both is Kingdom Hearts: 358/2 Days. The game, released after Kingdom Hearts, Kingdom Hearts: Chain of Memories, and Kingdom Hearts II, is an interquel set between the events of Kingdom Hearts and Kingdom Hearts II. However, it is also a side story, set concurrently with the events of Chain of Memories.