what are the definitions and the differences between the folowing words, when refering to forgiveness?:
- Salach סלח
- Machal מחל
- Nasah נסה/נשא
- Kaphar כפר
- Kasah כסה
The Ramban to Bamidbar 14:17, citing Onkelos, explains that סלח means הנחת העונש, setting aside the punishment (seemingly disagreeing with the Rashba cited below, who seems to understand מחל to mean this). Abarbanel writes the same thing.
The Avudarham explains סליחה to mean that any vestige of הקפדה (grudge?) has been removed.
The Malbim in Ayeles Hashachar 356 (who cites many other examples of words that mean forgiveness) explains that סליחה means the complete erasure of the sin, as if it never existed and never happened.
R' Hirsch to Tehillim 25:11 explains סלח is related to צלח - while צלח means to reach a goal, סלח means to enable to progress towards a goal - forgiveness removes the obstacle which prevents a person from growing.
The Machane Ephraim in hilchos Zechiya Umatana cites the Rashba that מחילה means סילוק הטענה, removal of a claim. Machal means to forgo your right to exact punishment or take compensation, but does not mean that the infraction itself is forgiven.
Nachal Eshkol in the introduction writes that מחל comes from חלל, and he explains that it means to empty something out, to weaken it. In forgiveness, it means to water down the intensity of the sin.
I don't have anything about כסה in my notes.
From this article
נשא From a Hebraic perspective, the forgiveness of sins is the same as lifting it off and removing it just as we see in Micah 7:19.
He will again have compassion upon us; he will tread our iniquities under foot; and thou wilt cast all their sins into the depths of the sea.
The Hebrew word סלח (salahh, Strong's #5545) is also translated as forgive and is used in the following verse where the forgiveness of iniquity is being paralleled with the healing (or lifting up) of diseases.
Bless the LORD, O my soul, and forget not all his benefits, who forgives all your iniquity, who heals all your diseases. (RSV, Psalm 103:2,3)
By investigating other words that are related to סלח (salahh) we can see that this word has a very similar meaning to נשא (nasa). סלד (salad, Strong's #5539) means "to leap up." סלע (sala, Strong's #5553) is a "cliff" (a wall that is lifted up). סלק (salaq, Strong's #5559) means "to ascend."
"Strong" refers to Strong's Concordance with. Hebrew and Greek Lexicon
This article explains that מחל is a variant of מחה meaning "to wipe out" or "erase".
There are also genuine Aramaic words which have passed into Hebrew, sometimes in several forms. The Hebrew makhatz (“crush”) is found in the Bible (Judges 5:26), while its ancient Aramaic form is מחק (makhak). In a subsequent period, the same Aramaic root was taken over again into Hebrew in a later form מחא (macho – “to clap hands”), and finally re-entered Mishnaic Hebrew, changing both form and meaning as מחה (machot – “to protest,” actually by clapping the hand). Thus one finds in Israeli Hebrew a single Semitic root in four variations
כפר means "to cover". See this M.Y. question, Cognitive Meaning of "Kaphar"
כסה also means "to cover". Offhand, I have not seen this term used in the context of forgiveness. If you could cite a verse or other source where this is used, I may be able to explain its nuances.