Here is my even more meaningless (part) rebuttal (and part agreement). Sometimes "prequel" describes followups where it is not always possible to apply a label defined solely in terms of intertextuality. In the case of The Godfather Part II, the narrative combines elements of a prequel with those of a more generalized sequel by having two intercut narrative strands, one continuing from the first film (the mafia family story under the leadership of Michael Corleone), and one, completely separate, detailing events that precede it (the story of his father Vito Corleone in his youth). In this sense the film can be regarded as both a "prequel and a sequel" (i.e., both a prior and a continuing story), and is often referred to in this manner.
In the original Planet of the Apes series, even though the latter three films depict events chronologically prior to those of the first two films, the narrative itself is continuous, as three characters from the first two films go back in time. The later installments (Escape from..., Conquest of..., and Battle for...) are sometimes called "prequels" in a broad sense of the word, and they are also sequels defined both broadly (as later installments) and narrowly (as continuation of the previously established storyline).
In recent times the term "prequel" has also been applied to origin-story reboots, such as Rise of the Planet of the Apes, Batman Begins, and Casino Royale. The creators of both Batman Begins and Rise of the Planet of the Apes also stated their intent to dispense with the continuity of the previous films so they would exist as separate pieces of work, with Christopher Nolan—director of Batman Begins—explicitly stating he does not consider it a prequel. Here, "prequel" denotes status as a "franchise-renewing original" that depicts events earlier in the (internally inconsistent) narrative cycle than those of a previous installment. Most reviewers require that a prequel must lead up to the beginning of its original work, which is inconsistent with works that dispense with the narrative of previous work and are not significantly within the same continuity.
The 2009 film Star Trek features characters from the 1960s TV series Star Trek, but earlier in their careers. However, the film is set in an alternate timeline caused by a Romulan captain from the universe of the original series going back in time and interfering with history. Thus, the film has been described as simultaneously a prequel and a reboot.
