In the common context of a narrative work of fiction, a sequel portrays events set in the same fictional universe as an earlier work, usually chronologically following the events of that work. In video games, there is often no narrative at all to link a game to its sequel (for instance, Forza Motorsport and Forza Motorsport 2,) and many story-focused sequels drop some or all of the characters, settings, and themes found in the original game. Final Fantasy is well-known for introducing an entirely new world and cast of characters in every numbered sequel, although concepts like chocobos, summons, and even characters named Cid recur throughout the series.
A spiritual successor or spiritual sequel is an original game that takes heavy inspiration from a single game or series, without having any explicit connection to it. This can be a way for developers to make a quasi-sequel to a game they previously worked on, without needing to secure the rights to the brand - a notable example of this is Dark Souls, a game that is effectively a sequel to Demon's Souls, but was not published by Sony and thus could not use the Sony-owned Demon's Souls name.