Terminator Genisys is a highly-underrated entry in the Terminator series of movies about humanity's time-traveling battle against the evil artificial intelligence Skynet. The 2015 film, directed by Alan Taylor, has an unusually-spelled title that received derision from fans and publications when it was revealed in 2014. At first glance, the title seemed to be an egregious example of the kind of pointlessly stylized spelling that had been going out of fashion since the late '90s. However, the movie itself actually provides an explanation for the strange-looking name.
As it turns out, the "Genisys" of the title refers to an entity that plays an important role in the story of the film, but series fans who skipped this installment might not know what it is. Even so, there are still a few mysteries in the short title that the movie doesn't explain, which audiences have been left to theorize about.
In the pre-war scenes of Terminator Genisys, Skynet creator Cyberdyne Systems is a seemingly ordinary software company. After meeting in 1984, this movie's version of Kyle Reese and Sarah Connor time travel to 2017. There they meet a doctor who enthuses about Cyberdyne's upcoming operating system: Genisys. With Genisys being an operating system, it quickly becomes clear that the "Y" in "Genisys" represents an in-universe portmanteau of "genesis" and "system." Whether this pun justifies the controversial title is another question, but at least there is a plot-relevant reason behind it.
As for the "genesis" part, the operating system represents the genesis of Skynet itself. Kyle receives memories of his 12-year-old self saying that "Genisys is Skynet." An ominous interview with Genisys' inventor Danny Dyson reveals the operating system is also linked to the military, foreshadowing Skynet's apocalyptic nuclear missile launch. Danny justifies the product's name in-universe by describing it as "the dawn of a new age," but the name takes on a darker significance as the genesis of the series' ultimate villain, personified in this movie by Matt Smith.
One of the film's producers, David Ellison, likened the play on words to the name of real-life tech corporation Google, which is thought to be named after the mathematical "googol." In the same Q&A session, Ellison also pointed out that the film depicts the genesis of the human-terminator hybrid that legendary hero John Connor is shockingly revealed to have become. In fact, Jason Clarke's compellingly twisted version of John is revealed to have gone back in time to help Cyberdyne bring about Genisys' creation.
If Genisys is a pun on genesis and system, why is it not spelled Genesys? The answer is not as clear, but viewers can make a few logical estimations. Stack Exchange user Praxis plausibly argues that the "I" in the title represents the word "genius" because the new system is "smart." Thus, "genius" and "system" make "Genisys."
Alternatively, perhaps the additional misspelling is simply to prevent people from mispronouncing the title as "gene-sys," as proposed by commenter Lèse-majesté in the same thread. This would cause fans to miss the genesis part of the title and possibly think that Skynet's plot somehow involves genetic modification -- John's cellular transformation notwithstanding.
Whether fans think Genisys is a good title or not, it wasn't chosen thoughtlessly. Terminator Genysis is spelled the way it is because it incorporates the words "genesis," "system" and possibly "genius." However, this evidently wasn't apparent to the public when the movie's title was announced all the way back in 2014. It is little wonder that the next film in the series was simply titled Terminator: Dark Fate.