Parody: An imitation of the style of a particular writer, artist, or genre with deliberate exaggeration for comic effect.
Examples: Movie and music parodies are very prevalent in current times as they bring a sense of nostalgia (mainly with movies) and humour to past artists' works. The most known movie parodies have been (and still are): Scary Movie (series), Johnny English (series, UK's best in current generation), and Spaceballs (parody of Star Wars, greatest film at time of release). The most known parody music artists at the moment are: "Weird Al" Yankovic, The Midnight Beast (UK), and Rucka Rucka Ali.
Pastiche: An artistic work in a style that imitates that of another work, artist, or period.
Examples: George Lucas' influence for the Star Wars series was the film Metalstorm: The Destruction of Jared-Syn (1983). Ever since creation, Star Wars has been an influence on most post-modern movies. Queen's influence for Bohemian Rhapsody was Happiness is a Warm Gun by The Beatles.
Intertextuality: The interrelationship between texts, especially works of literature; the way that similar or related texts influence, reflect, or differ from each other.