There are three Hebrew words translated to forgive.
1. kaphar, “to cover” (Deut. 21:88Be merciful, O Lord, unto thy people Israel, whom thou hast redeemed, and lay not innocent blood unto thy people of Israel's charge. And the blood shall be forgiven them. (Deuteronomy 21:8); Psa. 78:3838But he, being full of compassion, forgave their iniquity, and destroyed them not: yea, many a time turned he his anger away, and did not stir up all his wrath. (Psalm 78:38); Jer. 18:2323Yet, Lord, thou knowest all their counsel against me to slay me: forgive not their iniquity, neither blot out their sin from thy sight, but let them be overthrown before thee; deal thus with them in the time of thine anger. (Jeremiah 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. 50:1717So shall ye say unto Joseph, Forgive, I pray thee now, the trespass of thy brethren, and their sin; for they did unto thee evil: and now, we pray thee, forgive the trespass of the servants of the God of thy father. And Joseph wept when they spake unto him. (Genesis 50:17)); and used of God as "forgiving iniquity and transgression and sin" (Ex. 34:77Keeping mercy for thousands, forgiving iniquity and transgression and sin, and that will by no means clear the guilty; visiting the iniquity of the fathers upon the children, and upon the children's children, unto the third and to the fourth generation. (Exodus 34:7); Num. 14:1818The Lord is longsuffering, and of great mercy, forgiving iniquity and transgression, and by no means clearing the guilty, visiting the iniquity of the fathers upon the children unto the third and fourth generation. (Numbers 14:18)); and in describing the blessedness of the man "whose transgression is forgiven, whose sin is covered" (Psa. 32:11<<A Psalm of David, Maschil.>> Blessed is he whose transgression is forgiven, whose sin is covered. (Psalm 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, 3520And he shall do with the bullock as he did with the bullock for a sin offering, so shall he do with this: and the priest shall make an atonement for them, and it shall be forgiven them. (Leviticus 4:20)
26And he shall burn all his fat upon the altar, as the fat of the sacrifice of peace offerings: and the priest shall make an atonement for him as concerning his sin, and it shall be forgiven him. (Leviticus 4:26)
31And he shall take away all the fat thereof, as the fat is taken away from off the sacrifice of peace offerings; and the priest shall burn it upon the altar for a sweet savor unto the Lord; and the priest shall make an atonement for him, and it shall be forgiven him. (Leviticus 4:31)
35And he shall take away all the fat thereof, as the fat of the lamb is taken away from the sacrifice of the peace offerings; and the priest shall burn them upon the altar, according to the offerings made by fire unto the Lord: and the priest shall make an atonement for his sin that he hath committed, and it shall be forgiven him. (Leviticus 4:35); Lev. 5:10, 13, 16, 1810And he shall offer the second for a burnt offering, according to the manner: and the priest shall make an atonement for him for his sin which he hath sinned, and it shall be forgiven him. (Leviticus 5:10)
13And the priest shall make an atonement for him as touching his sin that he hath sinned in one of these, and it shall be forgiven him: and the remnant shall be the priest's, as a meat offering. (Leviticus 5:13)
16And he shall make amends for the harm that he hath done in the holy thing, and shall add the fifth part thereto, and give it unto the priest: and the priest shall make an atonement for him with the ram of the trespass offering, and it shall be forgiven him. (Leviticus 5:16)
18And he shall bring a ram without blemish out of the flock, with thy estimation, for a trespass offering, unto the priest: and the priest shall make an atonement for him concerning his ignorance wherein he erred and wist it not, and it shall be forgiven him. (Leviticus 5:18); &c). It occurs in the prayer of Solomon at the dedication of the temple (1 Kings 8:30, 34, 36, 39, 5030And hearken thou to the supplication of thy servant, and of thy people Israel, when they shall pray toward this place: and hear thou in heaven thy dwelling place: and when thou hearest, forgive. (1 Kings 8:30)
34Then hear thou in heaven, and forgive the sin of thy people Israel, and bring them again unto the land which thou gavest unto their fathers. (1 Kings 8:34)
36Then hear thou in heaven, and forgive the sin of thy servants, and of thy people Israel, that thou teach them the good way wherein they should walk, and give rain upon thy land, which thou hast given to thy people for an inheritance. (1 Kings 8:36)
39Then hear thou in heaven thy dwelling place, and forgive, and do, and give to every man according to his ways, whose heart thou knowest; (for thou, even thou only, knowest the hearts of all the children of men;) (1 Kings 8:39)
50And forgive thy people that have sinned against thee, and all their transgressions wherein they have transgressed against thee, and give them compassion before them who carried them captive, that they may have compassion on them: (1 Kings 8:50). Also in Psa. 103:33Who forgiveth all thine iniquities; who healeth all thy diseases; (Psalm 103:3); Jer. 31:3434And they shall teach no more every man his neighbor, and every man his brother, saying, Know the Lord: for they shall all know me, from the least of them unto the greatest of them, saith the Lord: for I will forgive their iniquity, and I will remember their sin no more. (Jeremiah 31:34); Jer. 36:33It may be that the house of Judah will hear all the evil which I purpose to do unto them; that they may return every man from his evil way; that I may forgive their iniquity and their sin. (Jeremiah 36:3); Dan. 9:1919O Lord, hear; O Lord, forgive; O Lord, hearken and do; defer not, for thine own sake, O my God: for thy city and thy people are called by thy name. (Daniel 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. 10:1717And their sins and iniquities will I remember no more. (Hebrews 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. 4:3232And be ye kind one to another, tenderhearted, forgiving one another, even as God for Christ's sake hath forgiven you. (Ephesians 4:32)). So in the O.T., "I will heal their backsliding, I will love them freely" (Hos. 14:44I will heal their backsliding, I will love them freely: for mine anger is turned away from him. (Hosea 14:4)).
2. The guilty one is released, forgiven. "That they may receive forgiveness of sins" (Acts 26:1818To open their eyes, and to turn them from darkness to light, and from the power of Satan unto God, that they may receive forgiveness of sins, and inheritance among them which are sanctified by faith that is in me. (Acts 26:18)). "As far as the east is from the west, so far hath he removed our transgressions from us" (Psa. 103:1212As far as the east is from the west, so far hath he removed our transgressions from us. (Psalm 103:12)). "Your sins are forgiven you for his name's sake" (1 John 2:1212I write unto you, little children, because 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 1:99If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness. (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, 107So that contrariwise ye ought rather to forgive him, and comfort him, lest perhaps such a one should be swallowed up with overmuch sorrow. (2 Corinthians 2:7)
10To whom ye forgive any thing, I forgive also: for if I forgave any thing, to whom I forgave it, for your sakes forgave I it in the person of Christ; (2 Corinthians 2:10)). 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 20:22-2322And when he had said this, he breathed on them, and saith unto them, Receive ye the Holy Ghost: 23Whose soever sins ye remit, they are remitted unto them; and whose soever sins ye retain, they are retained. (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. 40:1-21Comfort ye, comfort ye my people, saith your God. 2Speak ye comfortably to Jerusalem, and cry unto her, that her warfare is accomplished, that her iniquity is pardoned: for she hath received of the Lord's hand double for all her sins. (Isaiah 40:1‑2); Luke 17:33Take heed to yourselves: If thy brother trespass against thee, rebuke him; and if he repent, forgive him. (Luke 17:3); James 5:15-1615And the prayer of faith shall save the sick, and the Lord shall raise him up; and if he have committed sins, they shall be forgiven him. 16Confess your faults one to another, and pray one for another, that ye may be healed. The effectual fervent prayer of a righteous man availeth much. (James 5:15‑16); 1 John 5:1616If any man see his brother sin a sin which is not unto death, he shall ask, and he shall give him life for them that sin not unto death. There is a sin unto death: I do not say that he shall pray for it. (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. 6:14-1514For if ye forgive men their trespasses, your heavenly Father will also forgive you: 15But if ye forgive not men their trespasses, neither will your Father forgive your trespasses. (Matthew 6:14‑15)).