Loving can involve moonlight and roses but it can also involve kindness and care offered to somebody of whom we are not particularly fond. Love is an act of the will, deciding and wanting something good for somebody else. It doesn't necessarily involve affection. That's why Jesus can tell us to love our enemies. He's asking us to do good to them even if they want and do no good for us, even if our emotions find them repulsive.
Forgiveness is a subdivision of love.
It means loving in spite of the evil that another may have done to me. Forgiving does not involve pretending that no evil has been done or that the harm we have suffered really didn't hurt us. It does not require us simply to forget what has happened as if it never was. No, forgiveness allows us to be quite explicit and quite realistic about the harm we may have suffered, but it calls us to want and do good to the person who inflicted the harm in spite of what the person has done. Our Catholic Christian faith calls us to love and forgive, and the reason it calls us to love and forgive is because of who and what we are.