A — 1: καταλλάσσω
(Strong's #2644 — Verb — katallasso — kat-al-las'-so )

properly denotes "to change, exchange" (especially of money); hence, of persons, "to change from enmity to friendship, to reconcile." With regard to the relationship between God and man, the use of this and connected words shows that primarily "reconciliation" is what God accomplishes, exercising His grace towards sinful man on the ground of the death of Christ in propitiatory sacrifice under the judgment due to sin, 2—Corinthians 5:19 , where both the verb and the noun are used (cp. No. 2, in Colossians 1:21 ). By reason of this men in their sinful condition and alienation from God are invited to be "reconciled" to Him; that is to say, to change their attitude, and accept the provision God had made, whereby thier sins can be remitted and they themselves be justified in His sight in Christ.

Romans 5:10 Romans 5:11Mark 3:5Matthew 5:242—Corinthians 5:18-201—Corinthians 7:11
A — 2: ἀποκαταλλάσσω
(Strong's #604 — Verb — apokatallasso — ap-ok-at-al-las'-so )

"to reconcile completely" (apo, from, and No. 1), a stronger form of No. 1, "to change from one condition to another," so as to remove all enmity and leave no impediment to unity and peace, is used in Ephesians 2:16 , of the "reconciliation" of believing Jew and Gentile "in one body unto God through the Cross;" in Colossians 1:21 not the union of Jew and Gentile is in view, but the change wrought in the individual believer from alienation and enmity, on account of evil works, to "reconciliation" with God; in Colossians 1:20 the word is used of the Divine purpose to "reconcile" through Christ "all things unto Himself ... whether things upon the earth, or things in the heavens," the basis of the change being the peace effected "through the blood of His Cross." It is the Divine purpose, on the ground of the work of Christ accomplished on the Cross, to bring the whole universe, except rebellious angels and unbelieving man, into full accord with the mind of God, Ephesians 1:10 . Things "under the earth," Philippians 2:10 , are subdued, not "reconciled."

A — 3: διαλλάσσω
(Strong's #1259 — Verb — diallasso — dee-al-las'-so )

"to effect an alteration, to exchange," and hence, "to reconcile," in cases of mutual hostility yielding to mutual concession, and thus differing from No. 1 (under which see Lightfoot's remarks), is used in the Passive Voice in Matthew 5:24 , which illustrates the point. There is no such idea as "making it up" where God and man are concerned.

B — 1: καταλλαγή
(Strong's #2643 — Noun Feminine — katallage — kat-al-lag-ay' )

akin to A, No. 1, primarily "an exchange," denotes "reconciliation," a change on the part of one party, induced by an action on the part of another; in the NT, the "reconciliation" of men to God by His grace and love in Christ. The word is used in Romans 5:11; 11:15 . The occasioning cause of the world-wide proclamation of "reconciliation" through the Gospel, was the casting away (partially and temporarily) of Israel. A new relationship Godward is offered to the Gentiles in the Gospel. The word also occurs in 2—Corinthians 5:18,19 , where "the ministry of reconciliation" and "the word of reconciliation" are not the ministry of teaching the doctrine of expiation, but that of beseeching men to be "reconciled" to God on the ground of what God has wrought in Christ. See No. 1, above.

Leviticus 8:15Ezekiel 45:20