Here is how I have come to distinguish between an EXILASITO and a HILASTERION:
* an "atonement" is something done by *the perp*;
* a "propitiation" is something done by the *judge*;
* an "atonement" is an appeal for forgiveness though an expression of remorse;
* a "propitiation" is intended to appease the objections of the public (particularly those left unavenged) for the pardoning of the wicked;
* an "atonement" is a demonstration TO a judge;
* a "propitiation" is a demonstration *by* a judge;
* an "atonement" is made to recommend a penitent to a judge;
* a "propitiation" is made to recommend a judge to the wronged;
In no case and at no time is either an "atonement" or a "propitiation" conceived of as a **commercial** transaction, where sin is "paid for". Both atonement and propitiation are *gestures* in the context of the dispensation of *mercy,* not in the fulfillment of justice.
The death of Jesus is **never** spoken of in scripture as an "atonement" and no offering by a sinner is ever considered in scripture as a "propitiation." Confusion of these terms is the opposite of "rightly dividing."
The only "debt" that is in view in the propitiation was God's own obligation as judge, to repay the wicked for their deeds:
Ro 12:19 Dearly beloved, avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is mine; I will repay, saith the Lord.
When God **freely forgave** sinners and pardoned them, releasing them from punishment, God opened himself up to the charge that he was **negligent** in his duty as judge, scandalously leaving victims unrequited. What if Jesus let Hitler off at the last minute, based on his faith? Would not the Jews have a grievance with the judge? So the propitiation was to justify **God** rather than sinners.
As an individual, as judge has the right to freely forgive those who offend him. As a public servant, a judge must not be remiss in dispensing punishment to avenge victims. So God, willing to forgive (and often having done so in the past) HAD to give a demonstration of his commitment to public justice, which he did, by setting forth his son as a propitiation. In so doing he demonstrated that he was forgiving freely, but not without likewise bearing injustice in the form of the abuse of his son.
This is a very key passage:
Romans 3:24 Being justified freely by his [God's] grace through the redemption [release] that is in Christ Jesus:
25 Whom God hath set forth to be a propitiation through faith in his blood, to declare his [God's] righteousness for the remission of sins that are past, through the forbearance of God;
26 To declare, I say, at this time his [God's] righteousness: that he [God] might be just[ified], and the justifier of him which believeth in Jesus.