Spiritual Sequel
A spiritual sequel, sometimes called a spiritual successor, is a successor to a video game, movie, novel, comic, stage play, or television mini-series. Instead of being a standard sequel, spiritual successors share genres, themes, styles, and often developer teams, without continuing on a previous story. While this term can apply to almost any content, it has most commonly been used in video games.
Bio Shock is the spiritual sequel to System Shock.