Subjective of course, but for genres in which plots are important, a sequel is the continuation of the plot, following chronologically the events of the former. Main characters do not necessary need to be the reoccurring element, instead sequels can be about a location, a reoccurring monster or something else that continue from the previous titles. In those cases we can speak about a new story or stand-alone sequel.
Games specifically focused on gameplay such as simulations or strategy games tend to have sequels that enhance the gameplay instead.
A spiritual sequel or successor isn't a continuation. Risen isn't a continuation of Gothic, but a spiritual successor. Bioshock isn't a sequel of System Shock but a spiritual successor. Dragon Age isn't a sequel of Baldur's Gate or Neverwinter Nights but a spiritual successor. The differences between the former and the latter in these cases are huge, but the similarities are also easily spotted by the fans. Spiritual successors are usually made by the same company after they lost their license.