To forgive is to forget ... but if you forget then have you forgiven?
Niether are the same, I've always held to the saying, "forgive, but never forget." This philosophy comes from the old saying, "fool me once shame on you, fool me twice shame on me." Forgetfulness is a folley we put into service by eather our own mental failing or need for a false sence of closure. Forgivness is a willingness to make amends from the heart. Because it takes a heart to reoffer yours to one who has wronged you, in order to bring both partys back to a common ground of friendship. But it takes a failing of the mind to forget it even happened, or if you are willing to suffer it again to gain the favor and/or acceptance of your oppressor.
A turtle once told me: "Wise man say, forgiveness is devine, but never pay full price for late pizza!"