FGO chapter Salem, aka chritian guilt simulator 2020, is primarily about the relationship between sin, guilt, and punishment.
One of the most important characters of the chapter is Sanson, creator of the guillotine. He's certainly committed a sin; as an executioner during the Terror, he's killed his fair share of people, some of which innocent. And he feels a lot of guilt over it. But he's lacking in punishment; he wants to atone for his acts, which in Salem presents itself both as wanting to help the townpeople and as voluntareely putting himself in painful situations (such as: literally dying even when Circe could have saved him). He has the sin, the guilt, and wishes he had the punishment.
The other important figure is, obviously, Abby. Abiguail Williams, girl who historically kickstarted the Salem trials. She has the punishment; she has to witness atrocities unable to change anything, many of the victims being people she hold dear. She has the guilt, for sure. But (at least in this chapter) she has committed no sin, or no sin other than being a curious child. She says it herself: "if only I were a witch, if only I truly were wretched, if only I'd turned my back to God." She has the guilt, the punishment, and thus wishes she also had the sin, so at least it'd be justified.
But then, can you have the sin and the punishment without the guilt? The closest exemple I can think of in this chapter is Mata Hari; she does have the sin (got a bunch of soldiers killed) she does have the punishment (gets executed,) but she holds no guilt. She says it herself at the end of her trial: though she may have gotten people killed, she did what she thought was right at the time. She does not argue against her punishment any further. And thus, in Salem, once she has been appropriately punished as required by the village's customs, she is free from her role and can fuck around as she pleases.
Of the three, Mata Hari is not only the happiest, but also the most useful. Abigail is powerless until she snaps, Sanson is no longer of any help after dying, but Mata Hari is still around investigating and fighting and overall being involved in the story. It's not because she dodged punishment; it's because guilt doesn't achieve shit. Guilt will make you hungry for punishment to atone for your sins, but there is no metric to judge how much pain is worth a given sin. So you'll keep craving it, craving it, craving it, making yourself miserable, making the people around you miserable, and not even fixing shit on the way. That's the difference between guilt and responsibility. Responsability gets shit done.