I've been using the distinction that forgiveness is something I can do without the participation of the other person, while reconciliation is the restoration of relationship (I got my ideas originally from Forgiveness Forum). But someone in my Sunday school class brought in a sermon on reconciliation that gave the definition truth + forgiveness = reconciliation.
It would be wonderful if the other person admitted the truth of what happened or there was some other kind of public recognition of the truth. Certainly many people who write about their childhood abuse experiences are wanting just that: public recognition of the truth. But there is only limited room for that in this world. Is it possible to feel that the truth has been said without either an admission from the abuser or public recognition? It would take a kind of internal confidence I don't have yet; I've been discovering I don't expect people to believe me (when what I have experienced in recent years is that they do).
I'm realizing that it comes back to forgiveness. I don't want full restoration of relationship; I don't want to give that gift to the other person if they have not acknowledged the truth or asked for forgiveness. But that then sounds like another level of forgiveness to work on, because I am still wanting the other person to pay a price. I would like to get to the point where I'm not still wanting to hurt that person back. I can see that step is both hard and hopeful, to sacrificially absorb the evil.