The ḥaṭṭāʾth (Lev 4:1–5:13) answers unintentional sin, graded by office, anointed priest, whole congregation, ruler, common person (Lev 4:3, 13, 22, 27), with blood on the horns of the altar and, for priest and congregation, sprinkled before the veil (Lev 4:6–7); the same rite, on the same Day of Atonement, scales to cover the whole nation at once.
The ʾashām (Lev 5:14–6:7) answers trespass "in the holy things of the LORD" or against a neighbour, and requires restitution: the principal restored "and shall add the fifth part more thereto" (Lev 5:16; 6:5). Two threads run forward: the LXX's fixed sin-offering formula peri hamartias is the phrase Paul uses at Rom 8:3; and Isaiah 53:10 makes the servant's soul an ʾashām: the technical reparation term, not a loose metaphor.
What the ḥaṭṭāʾth blood accomplishes is genuinely contested: Milgrom's purification-offering thesis (the blood purges the sanctuary of accumulated impurity, not the offerer's guilt) against the classic expiation reading (the offerer's own sin is purged), the same fault line as the propitiation/expiation dispute on this page's hinge section, since both turn on what kāphar actually does to blood. Both positions stand attributed, neither silently adjudicated. Sources: KJV (PD); Jacob Milgrom, Leviticus 1–16 (Anchor Bible, 1991, cite-only).