It’s the difference between forgiving and forgetting. The first is a matter of being able to settle your own heart and let go; most people mistake it as meaning that it’s OK for someone who hurt you to do it again, but it has literally zero to do with anyone else. A purely internal process of healing and releasing yourself from the pain and the reaction.
The second — also often mistaken, this time for “carrying anger or hatred” — is nothing of the sort; only a calm refusal to deal with that person on those grounds (assuming the problem was intentional, or likely to be repeated.)
Healthy behavior, on the outside, can look identical to the other kind — but the processes under the covers are radically different.