Atonement vs Expiate - What's the difference?

As a noun atonement

is a repair done for the sake of a damaged relationship.

(transitive|or|intransitive) to atone or make reparation for.

(en noun)

A repair done for the sake of a damaged relationship.

The reconciliation of God and mankind through the death of Jesus.

* blood atonement * limited atonement * vicarious atonement

(transitive, or, intransitive) To atone or make reparation for.

* Clarendon

The Treasurer obliged himself to expiate the injury.

* 1888 , Leo XIII, "",

Thus those pious souls who expiate the remainder of their sins amidst such tortures will receive a special and opportune consolation,

* 1913 , ,

I am going out to expiate a great wrong, Paul. A very necessary feature of the expiation is the marksmanship of my opponent.

To make amends or pay the penalty for.

* 1876 , ,

He had only to live and expiate in solitude the crimes which he had committed.

(obsolete) To relieve or cleanse of guilt.

* 1829 , , Larcher's Notes on Herodotus , vol. 2, p. 195,

and Epimenides was brought from Crete to expiate the city.

To purify with sacred rites.

* Bible, Deuteronomy xviii. 10 (Douay version)

Neither let there be found among you any one that shall expiate his son or daughter, making them to pass through the fire.

Intransitive use, constructed with (for) (like (atone)), is obsolete in Christian usage, but fairly common in informal discussions of Islam.