Summary of Scripture Words.
Propitiation, Justification.

Propitiation.

This word is translated from the Greek Hilastërion, has the meaning of "to make amends for sin, to appease by sacrifice." It is also used in the New Testament for the "Mercy Seat", Hebrews 9:5,, this was the top lid of the ark of the covenant. It was the lid which was sprinkled with the blood of the sacrifice on the Day of Atonement.
Leviticus 16:14.

It is the thought that Jesus Christ completely satisfied the demands of a very Holy and Perfect God, as judgement for the sins of a person by His death on a cross. God now looks at the cross and all He sees when He looks at a person is a perfect person with no sins, they are covered by the blood which was shed on the cross,
Romans 3:23-26.

"23 For all have sinned, and come short of the glory of God;
24 Being justified freely by his grace through the redemption that is in Christ Jesus:
25 Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God;
26 To declare, I say, at this time his being right with God,righteousness: that he might be just, and the justifier of him which believeth in Jesus."

Propitiation is not to satisfy a vengeful God, it is to satisfy the righteousness of a pure and holy God, so that He can show mercy and righteousness

Justification

The Believer is justified, i.e. treated as being right with God, righteous because of Jesus Christ, who knew no sin, then took the sins of each person upon himself on the cross, being "made sin for each of us", that then meant that we became right with God, righteousness of God in Jesus,
2 Corinthians 5:21

"21 For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him."

Justification is actually an act of divine reckoning, it does not mean that the person has become righteous. The action of Justification is through Grace,
Romans 3:24.

"24 Being justified freely by his grace through the redemption that is in Christ Jesus:"

This action is by faith, not by works,
Romans 5:1.

"1 Therefore being justified by faith, we have peace with God through our Lord Jesus Christ: "

This is the act of God who has justly declared that a person is as righteous as the one who has belief and trust in Jesus Christ, this has been declared by the Judge himself and therefore nothing put upon themselves,
Romans 8:1.

"1 There is therefore now no condemnation to them which are in Christ Jesus, who walk not after the flesh, but after the Spirit."