Sixth movie: Same production as the 5th film, but with the help of James Cameron's Lightstorm Entertainment (Paramount distribution in the US, Fox/Disney worldwide)
This also led to the first two being released in home video by a plethora of companies. The first film's distribution ended up being the wildest, going from HBO to Hemdale to Live (under license from Epic) to MGM.
James Cameron was contractually obligated to give T2 to Orion to option, but the filmmaker's asking price was so high that the studio had no choice but to pass. It is a fact that Cameron, Schwarzenegger, and producer Gale Anne Hurd despised Orion's treatment on the first film (although it was a hit), that the high asking price has been perceived to have been deliberate so they wouldn't have to work with the studio again. If the situation was different, Orion might have released both films.
Of a very scary sort. The British Ministry of Defence actually operates a satellite network used to coordinate unmanned vehicles - including "Hunter Killer drones" - called SkyNet.
The US Air Force has a unit readiness tracking system called, I shit you not, SkyNet. During exercises, announcements come over the loudspeakers for group commanders to "update numbers in SkyNet".
There is a company called Cyberdyne that is working on exoskeletons. Based in Japan. The version it's getting the most attention for is called the HAL 5. Also, none of their projects involve AI. Although the Cyberdyne name isn't meant to be a reference, as they work in Cybernetics, and dyne is a suffix meaning power. Doesn't explain the HAL 5's name, though.
HAL is an acronym. It stands for "Hybrid Assistive Limb".
If parts of T4 gave you nightmares then just skip this link. At least there's no... teeth.
News 4 in Tucson, Arizona has a weather, traffic, and safety observation network called Skynet:  They have billboards for it all over the city and it's a bit unsettling. (Especially when in The Sarah Connor Chronicles the Los Angles traffic system was originally destined to be the "nervous system" of Skynet.)
God Does Not Own This World: The rights at first were equally shared between James Cameron and the first film's co-writer\producer Gale Anne Hurd. By the second movie, Cameron's part was with Carolco, which went belly-up. The two producers who formed Carolco (and went on to form C2) purchased the Cameron share in the company's liquidation auction in 1998 and Hurd's share one year later. To prevent the eventual subversion of the trope, as once the first movie turned 35 the rights would revert to Cameron, the Genisys producers who currently own the franchise went to get his help for the sixth movie (although he only produces and helped create the story, as the Avatar sequels kept him busy).
John Connor has been portrayed by numerous actors; with 7 actors playing him in 4 movies and a TV show. Sarah Connor was recast for the T:SCC series as well, with Lena Heady taking the iconic role from Linda Hamilton and ironically sharing the same initials.
T4 also has a new Kate Brewster and Kyle Reese; understandable and necessary in the latter case, since he's several years younger than in the original film.
Then came Genisys, which recasts Kyle, John and Sarah.
Word of Saint Paul: The novelizations of the first two films were written by a close personal friend of James Cameron, who had also contributed rough ideas to the concept. Some of the details revealed in the novels are confirmed true in later films, in creator interviews, or in other works—for example, the series of Terminator that is after Sarah. It was only called a T-800 in Terminator Genisys (the fifth movie, 21 years after the original!), but the novel refers to it as a Series 800.