I can't help but think of verses like this one.
1 John 2:2 And he is the propitiation for our sins: and not for ours only, but also for the sins of the whole world.
This requires understanding the differences between singular/plural anarthrous/articular hamartia (sin), along with hamartano (the verb) and hamartema/ta (the resulting acts of the verb).
The reason you don’t understand Hamartiology (like most others) is, quite frankly, because the church at large has never done much of a job of teaching it beyond basic shallow concepts.
Jesus was made sin (every aspect of the sin state of being for all mankind), and thus is the propitiation (in potentiality) for the sinS of the whole world. This is why the fire is effective as mercy for the unredeemed in the lake of fire.
Here you seem to be referring to original sin. Am I correct?
Well... I don’t prefer the term or concept of original sin from the Augustinian perspective, because Uncle Augies was not very good at expressing what it actually is. It’s really to be understood in the sense of negation, as in “Lack of original righteousness”. Sin isn’t a “something”, it’s something missing. So sin is a something like a hole is a something. So most confuse “Original Sin” as a weird kind of “something”, and that it was this thing that was added to man like some intangible tumor on his nature.
What I’m saying is that the missingness and lack in the unredeemed is not something that ever be filled after physical death while in their spiritual death. Thanatos (death) as a lack of communion means all that is necessary to fill that void that is sin is not available to them. Christ is the only means of administering this, and that’s done by being hypostatically joined to Him in this physical life.
But here you seem to be talking about sins again, and I see a multitude of verses that address Jesus Christ being the saviour of all men, but I guess that would fall under the idea that it's a different kind of salvation.
It’s the difference between sin as a state of being and sinS as the resulting actions from acting.
Since the unredeemed in the lake of fire can never have their ontology changed (their ousia/being and its physis/nature), then the only relief at all is the fleeting setting apart of the torment within them from the actions they have committed. They bear the torment of the guilt and remorse, etc. This is the torment, and it’s primarily internal. Most perceive the torment as external and physical, when this is not a physical place in the sense that we understand from the cosmos.
It’s much the same idea as a hug giving some kind of external comfort that has a fleeting temporary internal effect, but the grief or pain or sadness inside is not abated. This is maybe as close as words can come to describing this.
1 Timothy 4:10 For therefore we both labour and suffer reproach, because we trust in the living God, who is the Saviour of all men, specially of those that believe.
This is Objective Justification versus Subjective Justification. Related to Unlimited Atonement, but not in the Arminian sense.
Savior of sin (the state of being).
I'm not seeing much change in the physical life of believers. Maybe I'm missing what you're saying here.
Well... That’s my concern, too. There are too many false gospels and too much false doctrine. Few understand or even want to know the truth if it differs with their own acquired beliefs; and few have a valid source for their beliefs.