A basic meaning of the New Testament word ‘forgive’ is ‘release’ or ‘cancel’, as with a debt. Hence the ESV of the Lord’s Prayer says: ‘forgive us our debts, as we also have forgiven our debtors.’ To ‘forgive’ a debt means promising that you won’t ‘call it in’.
But that doesn’t mean pretending the wrong never happened. Cancelling a debt doesn’t mean you have to lend again. Hence Jesus highlights the importance of repentance, e.g. Luke 17.3: ‘If your brother sins, rebuke him, and if he repents, forgive him, and if he sins against you seven times in the day, and turns to you seven times, saying, “I repent,” you must forgive him.’
We can ‘forgive’ in the most basic sense (‘release’) by ourselves, before the offender repents (cf. Mark 11.25). And if that forgiveness is genuine, it will welcome repentance. And that repentance paves the way for some form of reconciliation (but not necessarily a return to the way things were before the offence, cf. 1 Corinthians 7.10-11).
So three Rs of Forgiveness are Release, Repentance and Reconciliation. And not accidentally, that’s exactly the kind of forgiveness we find in the Gospel. Jesus has released us from our debt, which he cancelled at the cross (Colossians 2.14). He now ‘commands all people everywhere to repent’ (Acts 17.30). And everyone who does this is reconciled to him (2 Corinthians 5.18-20).