A — 1: ἀφίημι
(Strong's #863 — Verb — aphiemi — af-ee'-ay-mee )

primarily, "to send forth, send away" (apo, "from," hiemi, "to send"), denotes, besides its other meanings, "to remit or forgive" (a) debts, Matthew 6:12; 18:27,32 , these being completely cancelled; (b) sins, e.g., Matthew 9:2,5,6; 12:31,32; Acts 8:22 ("the thought of thine heart"); Romans 4:7; James 5:15; 1—John 1:9; 2:12 . In this latter respect the verb, like its corresponding noun (below), firstly signifies the remission of the punishment due to sinful conduct, the deliverance of the sinner from the penalty Divinely, and therefore righteously, imposed; secondly, it involves the complete removal of the cause of offense; such remission is based upon the vicarious and propitiatory sacrifice of Christ. In the OT atoning sacrifice and "forgiveness" are often associated, e.g., Leviticus 4:20,26 . The verb is used in the NT with reference to trespasses (paraptoma), e.g., Matthew 6:14,15; sins (hamartia), e.g., Luke 5:20; debts (see above) (opheilema), Matthew 6:12; (opheile), Matthew 18:32; (daneion), Matthew 18:27; the thought (dianoia) of the heart, Acts 8:22 . Cp. kalupto, "to cover," 1—Peter 4:8; James 5:20; and epikalupto, "to cover over," Romans 4:7 , representing the Hebrew words for "atonement."

Matthew 6:12Matthew 18:21,22Matthew 18:15-17Luke 17:3Matthew 12:32,21—John 5:16 FORSAKELAYLEAVELETPUT
A — 2: χαρίζομαι
(Strong's #5483 — Verb — charizomai — khar-id'-zom-ahee )

"to bestow a favor unconditionally," is used of the act of "forgiveness," whether Divine, Ephesians 4:32; Colossians 2:13; 3:13; or human, Luke 7:42,43 (debt); 2—Corinthians 2:7,10; 12:13; Ephesians 4:32 (1st mention). Paul uses this word frequently, but No. 1 only, in Romans 4:7 , in this sense of the word. See DELIVER.

Luke 6:37DISMISSRELEASE.
B — 1: ἄφεσις
(Strong's #859 — Noun Feminine — aphesis — af'-es-is )

denotes "a dismissal, release" (akin to A, No. 1); it is used of the remission of sins, and translated "forgiveness" in Mark 3:29; Ephesians 1:7; Colossians 1:14 , and in the AV of Acts 5:31; 13:38; 26:18 , in each of which the RV has "remission." Eleven times it is followed by "of sins," and once by "of trespasses." It is never used of the remission of sins in the Sept., but is especially connected with the Year of Jubilee (Leviticus 25:10 , etc.). Cp. the RV of Luke 4:18 , "release" (AV, "liberty"). For the significance in connection with remission of sins and the propitiatory sacrifice of Christ, see A, No. 1. See DELIVERANCE , LIBERTY , RELEASE , REMISSION. Cp. the different word paresis, "a passing over, a remission," of sins committed under the old covenant, Romans 3:25 . The RV should be used here. This passing over, or by, was neither forgetting nor "forgiving;" it was rather a suspension of the just penalty; cp. Acts 17:30 , "the times of ignorance God overlooked," RV; see also, e.g., Psalm 78:38 .