I've talked about the gods a few times before, if you want to use the search bar, you can probably find my past posts.
Anyway, the gods and users seem connected:
- USER1 seems to be the First god mentioned, aka The Callous, The Lust Eater, Nozomu, and likely HOPE. Tends to talk in all caps "LIKE THIS". It's season is Summer.
- USER2 is likely the Second god mentioned, aka The Calm, and The Wire god. Tends to talk in all caps with slants "/////LIKE THIS". It's season is Winter.
- USER3 is the Third god mentioned, aka The Concerned, The Dark, and later on calls itself Pareidolia. Tends to talk in lower case, but can change it up whenever apparently. This is likely the one you saw talking in lower case. It's season is Spring.
Terminal 23 seems to be this World, but it isn't exactly clear yet. USERS and gods are somewhat interchangeable.
Why the First god aka The Callous shares a name with Sensei's brother isn't clear, but it's possible that it is simply the name the Narrator chose to give it. Nozomu can translate to Hope. Not to mention, who the Narrator telling us about the gods, is, also isn't clear. Also, probably should mention that USER1 has apparently account shared before, which makes things even more confusing.
As for what USER2/The Second god seems to want? Well, presumably it wants order:
Out of all of the gods and USERS, this one seems be the one behind the resets, memory alteration, and perception alteration that's likely going on. It's been noted that this god can:
At least alter visuals, and certain events like 'The Scary Room' Main Event, show that Maya at least thinks it could reset her. Not to mention, stuff like affection points seem to be it's thing. The game parts of this game seems to be it's domain.
Overall: It's not impossible that The Second god may be the system itself, or at least has control over it.
The First god seems to want this power, hence HOPE being implied to want something to do with wires and Sensei's special ability. Ironically, this Callous god may be the only one that's actually on Sensei's side, at least in theory, whether that's a "good" thing is up to you.
The Third god on the other hand seems to just want to make things how it thinks things should be.
Also some notable spoilers are
that all 3 of these gods apparently gave Sensei his body, can't feel on their own, and require sacrifices that more or less translate to Sensei taking things that don't belong to him. They seem to need Sensei to fuck specific girls to maintain their power.