Note that I do believe that the books and the games are separate continuities, but part of the same canon. This means that while the events might be different, from number of minors maimed to character personalities in their entirety, rules are the same. The same gist as how MatPat describes it. Example: Charlotte is a robot and doesn't know it in the books. She isn't in the games, but now we know that humans can become robots and not know it. Elements of one continuity help piece together a canon to understand the other continuity better. Now to the theory.
Okay, so this one's probably the theory I'm most convinced of. It is my personal belief that William Afton/Springtrap and Glitchtrap are separate entities. Let's begin.
To start off, the reason I don't think they are one and the same is their behavior. Although William was a fairly sneaky guy, through his opening lines in Sister Location, as well as his behavior and/or lines in FNAF 3, FFPS, and AR, we can infer that William is a very much aggressive person in general. Examples:
When 'the board' asks him about the suspicious design of Circus Baby, William, rather than try to come up with some sneaky 'the claw is for ice cream' excuse, decides to make a more aggressive approach, actively ignoring the suspicious parts by going over the other features.
In FNAF 3, although he doesn't speak, he is clearly extremely aggressive, to the point where even though he is the only real threat in the building, FNAF 3 is still just as hard, if not harder, than its predecessors as well as successors. In other games, if the monitor is up, you won't know they are in the office until you put it down. William will make himself known, running in clear view, and while he hides in corners on cameras, he usually makes eye contact with the camera. Whereas other animatronics can usually be dealt with without maintaining eye contact, and once they're inside, you have at least a second or two to react. if you turn away when William is at the door, you have almost no time to play a sound. When he is in the office, he won't even let you keep the monitor up for that long.
In FFPS, although his voice is much more calm than his other voiced outing, AR, William is still clearly a very aggressive man. When he kills you, he mocks you, and he, along with everyone else, is very aggressive in trying to reach you.
In UCN, his Springtrap variation will stare you down from the vent. His Scraptrap variation will do the vent crawl equivalent of running towards a doorway screaming at the top of your lungs.
In AR, William is omega levels of aggressive, being one of the most unforgiving enemies in the game. His voice lines are extremely aggressive as well, talking loudly about how he WILL kill you, how you can't hide, he is superior, etcetera.
All in all, William is a very aggressive man. Now Glitchtrap... just isn't. He doesn't appear to make any attempt to attack you before you get the tapes. Even when he does infect/swap with you, he doesn't mock you, just calmly leaves. The most 'aggressive' he gets is during the mindswap sequence, and even then he just... moves his hands around. He's always in one of a few poses, unmoving unless another part of his code is returned in the tapes. The only time he shows any real activity is in Pizza Party, but I'll get to that in a minute. As for the 'I always come back. Let me out' line, I'll get to that, too.
So, what IS Glitchtrap, then? Here's my take:
Glitchtrap is just an advanced AI or virus IMPERSONATING William. Here's why:
William is still Springtrapping around in FNAF AR, which, given Vanny's behavior in the emails, takes place AFTER Help Wanted. And in Help Wanted, the tapes say that they scanned circuit boards, and that's where Glitchtrap came from. People tend to say that Glitchtrap came from a Springtrap circuit board. That's not possible. If Springtrap did get burnt up in FFPS, (not likely given his and other character's presences later on) his circuit boards would be burnt and crispy, unusable. If he SURVIVED (more likely. Fire has a track record of not working on him, and he's still vibing later on in AR.) then there is no chance the circuit boards came from him either, as he is very much hostile and would not allow someone to remove circuitry. This means Glitchtrap came from somewhere that isn't William.
And yes, people have told me there is more than one of Springtrap in AR, but that's just a gameplay mechanic that is unavoidable in this kind of game. There's multiple Circus Baby, too. The emails only refer to ONE 'vintage Bonnie model' randomly showing up to the homes of Fazbear Funtime Service subscribers. (FazFun subs for short.) As for the skins, William is a clever guy. He probably disguised himself. Same goes for Elizabeth.
Back to Glitchtrap. My theory is that he - IT, if I'm right - is a computer virus, just an incredibly advanced one. It is doing what any virus does to 'survive' and spread: Being a Trojan Horse. My guess is that in an uninfected, tapeless copy of the VR game, the model that is 'Glitchtrap' would still be present. This would be Pizza Party. This is the only time Glitchtrap is shown in a way that looks like a normal part of the game/doesn't glitch. So the virus seems to have used models of the Pizza Party Springbonnie to 'disguise' itself in a way that made it look like a normal part of the game. But it being just a virus, that's all it did, and according to the tapes, people noticed the model appearing in weird places. Then it latched to the tapes, infecting the files like any virus would. So as you get tapes, the virus is more 'complete'. As usual, it is evident only as still models and glitched animation loops (the tapes themselves and his appearance in the hub) until the tapes are reunited and the virus can spread. The Glitchtrap we see communicating with Vanny is most likely a similar thing to the visions illusion discs create: Vanny's mind fills in the blanks with the glitched models and animations in her head, creating a 'personality' accurate to what she THINKS William is like based on the knowledge she has. She never met the aggressive man that is Springtrap/William at all, so she only knows what she infers from the game she's testing and any exposure to the old newspapers: a cunning, charismatic man in a rabbit suit, who was smart enough to convince many children to follow him, and many adults to trust him. The voice she hears is the result of her mind, already vulnerable after Jeremy's gruesome death after succumbing to madness, interpreting the disturbing glitches that drove Jeremy insane in her own way, creating a voice in her head that speaks the way she'd expect William to speak. The 'I always come back' thing specifically points to this, as it’s a big line that always seems to be associated with William. She never heard the British accent, so when she hears the voice saying William’s catchphrase, it isn’t there. Essentially, her weakened mind combined the disturbing glitches with what she ‘knew’ about William Afton to create a split personality’s a a coping mechanism for dealing with the gruesome death of a coworker: ‘Glitchtrap’. It sounds far fetched, but it makes sense from a psychological perspective.
As for William himself, here’s my idea: he survives the FFPS fire, but barely. The time he spends recuperating after the fire is equated in the books as The Man in Room 1280, which seems to be the aftermath of the Fourth Closet, when Book William got yanked into a furnace. The ‘nightmares’ William experiences while recuperating after the FFPS fire are actually UCN. This explains a few things about UCN that don’t make sense, either under the ‘Cassidy torturing William in Hell’ theory specifically or just in general:
1: The Nightmare animatronics were figments of the FNAF 4’s kids imagination, so Cassidy, even if they’d found William’s memories of his kid talking about them, wouldn’t know enough about them to create the ones we see in UCN.
2: the fact that there are multiple cases of characters being the same animatronic at a different point in time. EX: the Withereds and Classics
3: the funtimes. Cassidy would’ve never even knew the Funtimes existed, especially not ENNARD.
All of these are things that make sense if it’s a nightmare in William’s head. Anyway, he comes back after a period of nightmare filled dormancy to recuperate, and goes on his way. He learns about the FazFun Service, and acts like part of it to disguise his activity. Circus Baby (and Ballora at this point, meaning Molten Freddy separated) probably did, too, and found a warehouse or something and got new suits to better hide in the roster. Plush trap is a real toy in the lore, so his presence is explained. Vanny, now struggling with her split personality she calls Glitchtrap, unaware that it isn’t a separate entity controlling her, starts displaying the weird activity we see in the emails.
So that’s my theory. Fairly farfetched, but after careful analysis, it makes more sense to me than any other options. Hope y’all enjoyed.