There are three Hebrew words translated to forgive.
1. kaphar, “to cover” (Deut. 21:8; Psa. 78:38; Jer. 18:23). It is also translated “atonement.”
2. nasa, “to bear,” take away [guilt]: used by Joseph's brethren when they asked him to forgive them (Gen. 50:17); and used of God as "forgiving iniquity and transgression and sin" (Ex. 34:7; Num. 14:18); and in describing the blessedness of the man "whose transgression is forgiven, whose sin is covered" (Psa. 32:1).
3. salach, “to pardon,” used only of the forgiveness that God gives. It is employed for the forgiveness attached to the sacrifices: "it shall be forgiven him" (Lev. 4:20, 26, 31, 35; Lev. 5:10, 13, 16, 18; &c). It occurs in the prayer of Solomon at the dedication of the temple (1 Kings 8:30, 34, 36, 39, 50. Also in Psa. 103:3; Jer. 31:34; Jer. 36:3; Dan. 9:19).
In the N. T. two words are used: ὔφεσις., from ἀφίημι, “to send from, release, remit,” several times translated REMISSION; and χαριξομαι, “to be gracious, bestow freely, forgive.” Both words are applied to the forgiveness granted by God, as well as that between man and his fellow.
There are two aspects in which forgiveness is brought before us in scripture.
1. The mind and thought of God Himself towards the sinner whom He forgives. On the ground of the sacrifice of Christ, God not only ceases to hold those who have faith in Christ's blood as guilty before Him, but His favor is towards them. "Their sins and iniquities will I remember no more" (Heb. 10:17). Thus all sense of imputation of guilt is gone from the mind of God. "God for Christ's sake hath forgiven you" ἐχαρίσυτο, graciously forgiven, (Eph. 4:32). So in the O.T., "I will heal their backsliding, I will love them freely" (Hos. 14:4).
2. The guilty one is released, forgiven. "That they may receive forgiveness of sins" (Acts 26:18). "As far as the east is from the west, so far hath he removed our transgressions from us" (Psa. 103:12). "Your sins are forgiven you for his name's sake" (1 John 2:12). Hence it is true of all Christians, that their sins are forgiven. Another thought is included in the forgiveness of sins, namely, that having redemption by Christ, which brings into a new state, the whole guilty past is forgiven, removed from us, so that there is no hindrance to the enjoyment of that into which redemption brings.
The general principle as to forgiveness is stated in 1 John 1:9: "If we confess our sins, he is faithful and just to forgive us our sins;" and to this is added, "and to cleanse us from all unrighteousness." This involves honesty of heart, whether in a sinner first coming to God, or in a child who has grieved the heart of the Father by sinning. The two aspects above referred to are here also. The faithfulness and righteousness of God in forgiving, and the cleansing us from all unrighteousness. God is faithful to His own blessed character of grace revealed in His Son, and righteous through the propitiation which He has made.
3. If a Christian is “put away” from the assembly and is repentant, he is forgiven and restored (2 Cor. 2:7, 10). This of course is different from the act of God in forgiving sins, and may be called administrative forgiveness in the church; and if the act of discipline is led of the Spirit, it is ratified in heaven: (Compare John 20:22-23). This is entirely different from any pretended absolution that may be pronounced over poor deluded unconverted persons.
4. There is also a governmental forgiveness in connection with the government of God here below in time, both on God's part, and toward one another (Isa. 40:1-2; Luke 17:3; James 5:15-16; 1 John 5:16). We are called upon to forgive one another; and if we indulge in a harsh unforgiving spirit, we must not expect our Father to forgive us in His governmental dealings (Matt. 6:14-15).