BOTH THESE WORDS ARE USED to express the idea of forgiveness. Apliiemi, the more common of the two, means basically to let go, to send away, and so when used to express forgiveness it signifies remission, as in Matthew 6. 12. ‘Forgive us our debts (i.e., remit them, do not exact payment) as we have forgiven our debtors (i.e. as we have let go, not exacted payment of (the debts) where our debtors are concerned)’.
Charizomai, which also can mean, among other things, to forgive, is a more colourful word. Basically it means to show oneself to be gracious, then to give something freely or graciously as a favour: so in Luke 7. 21, ‘and to the blind he granted sight’. So also in Galatians 3. 18 we read that God has given the inheritance to Abraham by an act of grace and favour and altogether apart from the works of the law (see also Rom. 4. 13). Finally it is used for remitting a debt, forgiving a trespass, as in Colossians 2. 13, where the emphasis is on the unmerited grace that cancels the debt.
Both words are used in the story in Luke 7. 40-50. When the debtors were unable to pay, the creditor frankly forgave: charizomai is used because it was an act of undeserved grace and favour, a meaning that the Authorized Version attempted to bring out by adding ‘frankly’ to ‘forgave’. In verses 47 and 48 aphiemi is used and here the emphasis is on the remission and discharge. This remission, too, was of course an act of absolute grace and favour and not in any way earned by the woman’s love. The parable shows that the debtors loved because they had been forgiven: they were not forgiven because they loved. Similarly with the woman: the Lord said, Wherefore I say unto you, Her sins, her many sins (not, as the Authorized Version, her sins which are many; there is no word representing ‘are’ in the Greek) have been forgiven (the tense is perfect). The ‘Wherefore’ is to be taken closely with the ‘I say unto you’. Christ is not telling Simon why the woman has been forgiven, but He was appealing to evidence that Simon could appreciate, to corroborate the truth of His statement that the woman had been forgiven. Thus: debtors, when forgiven their debts, love. This woman was a debtor, but now she loves. Wherefore, on this showing, I say she has been forgiven.