The Matrix and Terminator are two of the most popular science fiction movie franchises of all time. One of the more entertaining past times for science fiction fans is to wonder what if ... ? What if The Matrix and Terminator weren't in fact two of the most popular franchises but two sides of the same coin. One recent fan theory posits a theory based on that very hypothesis. The theory lays out the case for both stories actually being in the same timeline. It's one of the more interesting theories out there in the science fiction world and there are plenty of reasons to think that it actually makes quite a bit of sense.
The first thing to keep in mind is that the theory relies on another theory that movies and television shows are toying with more and more these days. That theory is an understanding in just how alternate timelines work. This of course, relies on the belief that there are all kinds of different realities where all kinds of different things can end up happening. In order to The Matrix and Terminator to exist in the same universe, some rather unfortunate first has to happen. In this particular timeline, the Terminator successfully kills Sarah Connor in the very first film of that franchise. By taking her out before she's able to give birth to John, something entirely different from what fans have seen in that movie franchise takes place.
With Sarah Connor gone and no John Connor to save the human race, the Terminator ended up doing his job very well. Skynet wins the war against the humans. In fact, it takes over the world despite some last-ditch efforts from the human race. Keep in mind that in The Matrix, humans are trying everything they can to fight back against the machines in what is ultimately a losing effort. Morpheus mentions that the machines eventually adapt and start to run on solar power. In turn, mankind decides to "scorch" the sky to try and take that energy source away. This is different than the original timeline where Sarah Connor survives and gives birth to John. Mankind never needs to pull out that last-ditch effort to win the way because John is there to lead them. In effect, the reality where the Terminator wins starts a branch of history that basically continues in The Matrix movies.
As the tale goes, the humans tried to blot out the sun in order to stop the machines in their tracks. What is actually Skynet learns to adapt and starts harvesting human beings in order to use as an alternate energy source. This part of the theory actually fits into at least a few scenes of some of the Terminator movies. Every so often, the humans are able to break a machine "encampment" only to find humans locked up as prisoners of war. This is always met with some confusion because it doesn't make a whole lot of sense for an army of killing machines to keep prisoners, but what if there is another reason why Skynet started locking people up? What if this was the beginning of the storing of humans to "recycle" later in order to use for energy? With John not there to stop them in the timeline where both movie franchises build on one another, John isn't there to defeat the machines and apparently stop this particular "humans are energy" plot that's been hatched and is carried out throughout The Matrix movies.
There are some problems with the idea that The Matrix and Terminator existing in the same universe. The first oddity of course, is that there's never a glimpse of the kind of humanoid machines Arnold Schwarzenegger is so famous for playing. Of course, this particular issue can be waved away with a rather simple explanation. The Matrix is well into the future when compared to the Terminator storyline. It's possible that the machines have realized that the form is shown facing off against Neo, Morpheus and the rest don't need to be humanoid. In fact, because humanity is living underground, the diggers are far more useful. Skynet is certainly well known for adapting to what it needs to do in order to win. The jump into the distant future would also explain why no one who is still alive ever mentions that the AI that started the way was called Skynet. That name could be lost to time.
The other big problem with this theory is that an offshoot of the original movies, the Animatrix is considered canon in that universe. In that animated version of The Matrix, the beginning of the conflict between machines and humans is shown in great detail. However, there is a way around this explanation as well. As viewers move from The Matrix to Matrix Reloaded to Matrix Revolutions, it becomes quite clear that portions of what actually happened in the original war have been forgotten, or erased from human history. This is why the humans don't realize Neo isn't the first messiah-type leader. It's why, in fact, there have been several people known as "The One" to come through their world. It doesn't take a giant leap to realize that perhaps the history of the war that is told in Animatrix is actually the history that the machines want people to think is the real history.
The big question if that was the case is why would whatever Skynet has become by the time viewers pick up the story in The Matrix, is why would it feel the need to erase the real history of the war. That honestly seems to be the best argument against the idea of Terminator and this other story being in the same universe. It's one that is really hard to explain away. By this period of time, it doesn't appear there would be any rhyme or reason for why it would wipe out the idea of the Terminator from humanity's memory. Of course, Skynet has its own motivations for all the things its done, including engaging in the war in the first place.