Here are six categories of language in the New Testament regarding atonement from Mark Dever’s sermon “A Biblical Understanding of The Atonement in the New Testament" [preached 3/16/1997].
1) Sacrificial and Ritual language. Including blood sacrifice language. [Ephesians 2:13; Colossians 1:19; Romans 5:9] Shepherd [John 10] who chose to die laid down His life for us.
2) Redemption, redeeming language. Pay ransom, to release from prison, or payment for good [market place language]. Also called financial language. Paid the price to set people free from bondage/chains to sin. [Matthew 6; 20; Acts 20; Romans 3:24]
3) Reconciliation language, relationally. Dealing with what estranged us, namely sin, on the cross. So dealing with sin and the extent and inner workings of what Christ did on the cross in order to reconcile us. [In John it speaks a few times of the “wrath of God [that] remains on them (John 3:36)”. Romans 5:6-8.] Also, it is God who reconciles…not us. [John 14… “Peace between God and man;” Romans 11:15; Ephesians 2:12… “Reconciled and brought near.”] A subcategory of this reconciliation would be “Adoption” language or “family” language.
4) Propitiation (Greek is hilasterion). God being satisfied so that He turns His wrath away. [see Leon Morris’ “The Atonement: It’s Meaning and Significance” book] [Luke 18:9… “be propitiated toward me”] Propitiation is relationally personal as opposed to expiation. Expiation isn’t bad, but it doesn’t handle the depth of propitiation. Expiation is just regarding a transaction, not intimate/personal/relational in any way. [Romans 3:25; Hebrews 2:17; 8:12]
5) Justification [due to I], language of the law court or legal and judicial language. [Luke 18; Acts 13:39]
6) Battlefield language [military language]. God’s victory in Christ. [Colossians 2:15… “principalities, powers, authorities;” Mark 3; Revelation 5:5; John 16:33; 19]. Warfare with demonic powers between God and the satanic world [Romans 8:39].
There's a ton more in Scripture, but this is what he had time to cover in his sermon [for the most part].