As pointed out in numerous fan works/discussions, this ignores the fact that a partially crushed Terminator arm is left behind when the ‘good’ Terminator is trashed by the T-1000. Of course, the novelization makes it clear they weren’t stupid enough to ignore it, but if we only go by what we see in the movie it is easily enough of a loophole to continue the loop.
The way I’ve always figured it is, as they say in T2, “There’s no fate but what we make for ourselves”. So the time line isn’t fixed (we’ve already seen changes), but, who is it who’s “making” this fate?
Sarah assumes she’s the one making the choices that determine the future, but it reality, it’s everyone in the world making those choices. Sure, her choices are probably more important than most individuals’ choices, because she’s central to the future history of Skynet and everything, and she has foreknowledge most of us lack, but even that can’t entirely outweigh the choices made by hundreds or maybe thousands of other people who are still interested in developing AI systems, for all the reasons we’ve ever wanted those systems.
Those choices are still pushing us towards the Skynet timeline, Sarah’s choices only deflect the course by a little bit, for a little while.
I can argue it up down and sideways, but was mostly expressing the attitude of the novels I was referencing.
Double spoilers just in case anyone wants to read the books down the road -
Summary
During the course of the novels, John learns that a pseudo-terminator is working with the government to build a next-gen non-AI computerized defense system (Skynet) and plans a daring raid to prevent it from happening. Sara decides that it is going to happen, whether by fate or human desire, (much like you suggest) but wants to let them have what they want WITHOUT letting it become an AI.
So John’s computer friends including girlfriend build a program that identifies pathways that would lead to sentience and a program that quietly shuts those down. They then raid the facility where the research is going down.
At the same time, the quasi-terminator learns that the computer expert doing the work isn’t gifted enough to create Skynet. And during the raid, comes upon the girlfriend who is uploading the first part of the program, which sets up the pathways prior to closing them.
Said GF is killed by the quasi-terminator, who destroys the AI preventing portion of the program, while John, finishes uploading the AI enabler thinking it’s the disabler.
So in this sequence, John is indirectly responsible for creating Skynet. Thus the ‘inevitability’ of the timeline I was mentioning.
Anyway, whether it be fate, the universe trying to keep the timeline intact, or the interweavings of countless human desires and hubris, it seems that universe is bound and determined to change the details but not the gross events of it’s history.
Which leaves out another fan question. The sequence of Terminator is already at least one revision - with a closed time loop at that. But nothing is to say it’s the first. It may be the twenty first. It may be the hundred and first.
But back to the OP - I agree with the novels and a lot of posters here, it makes no sense for Sarah and John to stay in the states. They are felons, and even if some people believe them, it’s a lot easier to ignore the problems and babblings (of a confirmed crazy person) and lock them away forever.
Even Dyson, who was WORKING with the Terminator remains, didn’t believe them until Ahhhnold shucked it’s arm coating. John’s juvie record and apparent closeness with the T-800 who has many, many assaults (of T2 as well as the lethal attacks of the first) is going to have him tried as an adult accessory as well, or involuntarily committed.
So did John Connor. So, who fathered him?
Not necessarily. In several models of time travel, each of the timelines continue to exist even after a history-changing event; so the original timeline is still out there, somewhere, and so are all the other alternates. So it is perfectly valid to imagine a post-T2 timeline as ‘continuing to exist’ even after events in the later movies retconned history. If these alternate histories didn’t exist somewhere, you would get a paradox, as there would be nowhere for Ahnold and T-1000 to come from.
Marty McFly.
Stranger
Near the beginning of the first Terminator, Sarah is complaining to her roommate that the guy she went out with the weekend before is standing her up. Perhaps she is already pregnant at the start of the movie.
And the person who left the message on her answering machine to cancel the date? James Cameron.
Think of how IT security professionals are creating new defensive tools and measures, and hackers are coming up with new ways to get around them. They are keeping close watch on each other and their tools and methods and continually trying to best each other in a never-ending cycle.
Now imagine that instead of hackers trying to infiltrate systems, they are killer robots trying to destroy humanity. But everything else is the same. So yeah, you’d know what models are out there, and keep close track of them the best way you possibly can. The average person just trying to live in a post-apocalyptic world wouldn’t know any of that stuff, but the people devoted to fight them (John Connor, Kyle Reese, and their colleagues) certainly would.
For that matter, it’s not that different from a real-life soldier being educated on the military equipment of the enemy. I mean, The Art of War was written in the 5th century BC, by Sun Tzu, and he said:
If you know the enemy and know yourself, you need not fear the result of a hundred battles. If you know yourself but not the enemy, for every victory gained you will also suffer a defeat. If you know neither the enemy nor yourself, you will succumb in every battle.
So even that guy from 2,500 years ago would advise knowing the different Terminator models.
Let me clarify my comment:
I can understand that they should know. My point was, I don’t think they could know. Skynet probably doesn’t publish tech data. Can you tell a CSM-101 from a CSM-102, with the improved duodynetic chipset? probably not. Chances are, you get close enough to spot the differences, you don’t live long enough to tell anyone
I also don’t think Cyberdyne/Skynet calls them Model 101, 102, T1, T1000, I think they call them long strings of machine code. OK, maybe the “101” is just what the humans call them, I can dig it. But the assembly line doesn’t have a big banner “10,000th CSM-101 built! Together we can wipe out the human infestation! Huzzah!” 
I actually appreciated that the chips in the recovered “101” terminator CPU didn’t have any markings. A fully automated production facility, run, stocked and built by machines doesn’t really need inventory control. The box of chips that came in last week are still where they were put, and the computer remembers. Nothing will ever get mixed up.
This also begs the question, why would Terminators need heads-up displays?
A very good question!
I always figured it was just a visualization of what the terminator was processing, not an actual HUD. But there’s nothing in canon that supports that. I’d be disappointed if they filmmakers really thought that was what a Terminator saw. 'twould be very inefficient.
I think the HUD is analogous to evolution in humans - it doesn’t necessarily produce the most optimized designs, just whatever works. The original robots created by humans had displays so humans could track what was happening and debug them. As the robots started building themselves, they continued to included HUDs because that’s how they’ve always been built.
They would be examining and reverse-engineering destroyed terminators. Even if there are no written notes on the machine, it will still have some way of showing its model number and other info for other robots to service them.
I think we can assume the existence of an alpha timeline where Cyberdyne created Skynet on its own and John Connor’s father was just some guy.
Well, as the audience we see that the 101 is your go-to Terminator when you need one that can punch above its weight and survive attacks by whatever advanced thing some alternate Skynet can throw at whomever you are trying to protect. It is absurdly durable and seems to know how to get things done.
101 refers to the skin, so the Arnie model. The T-800 part refers to the chassis. The T-850 from T3 was a more advanced chassis with nuclear batteries. It was also hardened against shock damage and had skin that grew back faster IIRC. The Sarah Connor Chronicles gave us the T-888 which was a smaller and lighter version. We never saw the 101 on the show because the skin wouldn’t have fit.
You are absolutely correct in that most characters should be dead several times over in the time it takes them to dwell on the differences. The most obvious example is in Salvation when Marcus calls out to a T-600 and stares at it dumbly while it shoots at him with a Gatling gun. I guess that’s the model with the glitchy targeting sensor.
In my personal Terminator canon, there is a “Prime” timeline where this is exactly what happened. Sarah gets pregnant by the usual means, calls the kid John and Skynet arises without any outside help. But since the first movie, this Prime timeline is completely paved over and they can never get back to it. Everything they ever do just puts them further way from it. We also see that Skynet is actively hopping between timelines bootstrapping itself.
In T2, when the bikers blow smoke at Uncle Bob his heads up display identifies it as “carcinogen vapor” which I have always taken as a weird PSA. The Terminator is warning you not to smoke! The killer machine from the radioactive wasteland of the future doesn’t want you to get cancer! There’s also the casualties HUD from the Cyberdyne shootout where Uncle Bob’s display advises him of 0.0 casualties. Because the way Skynet counts them, you can apparently have .5 of a casualty or something. I have a feeling the displays are 99.9 percent for the audience and the production team never really put much thought into why every Terminator thinks out loud visually and very slowly.
Perhaps this piece of information is not a PSA but simply a useful note for the Terminator.
I wonder if the government would create a special contingency force for post-skynet survival. Headed by Sarah and John Conner, it would be composed of special forces personnel who have been trained to help bring humanity back from the brink. Not just to fight Skynet, but to recover society overall. Everyone thinks that the Connors are looney, but also that it would be good to have a post-apocalypse organization in principle. A secret government organization of preppers.
Okay, the different universe thing. Let’s go with that.
Keep in mind that the T-800 lost an arm in that gear assembly, so some vestige of the technology was left. Also, in my opinion, the continuous development of computer technology would have inevitably lead to Skynet or some other version of it like Legend, as in Dark Fate. In either scenario, however, the Sarah Connor connection would have disappeared.
Unfortunately, due to her trauma and paranoia, I doubt she would have been capable of believing that. That, along with being highly wanted by law enforcement, would have probably kept her hiding out in Mexico or some other place that is pretty much off the grid, and she would have spent the rest of her life in hiding.
John, on the other hand, wasn’t pinned to the bulletin boards of every agency in the country as was his mother’s. The question is, would he have been too loyal to leave his mother alone, or would he have chosen to strike out on his own? I personally believe he would have stayed with her as long as she lived which, according to T-3, wasn’t a very long time.
How about the first movie, when Arnies in the hotel doing some self repair. The landlord knocks on the door, and we get a HUD view of the Terminator picking responses from a dialogue tree! (“Yes/No/Fuck you, asshole.”) Does he just have billions and billions of pre-written sentences that he picks from as necessary? Was the real reason he asked for that phased plasma rifle just that he was clicking through all the shop options to see what responses he’d get?
(Also, when I remembered this scene, I 100% recalled the HUD being CRT green. Nope. It’s red with white text. I blame The Matrix.)