I used to believe that those two were the same but since a few years ago I have come down closer to this.
That said I really do forgive even if I don't always forget:
- the person will get cake/discounts/etc and I won't seek revenge
- I might not however hire them / defend them / etc
I've struggled a bit with this and a number of similar problems since according to my religion there's no forgiveness for me unless I forgive others and I actually have a past so I better not void the deal ;-)