The two concepts, "love" and "forgiveness" are very different, though they may be related on some levels.
Love has been the subject of countless poems, songs, essays, novels, etc., and it means many different things to different people. Defined, it is...
... a feeling of warm personal attachment or deep affection, as for a parent, child, or friend...
...sexual passion or desire.
The term is used freely within society with regard not only to human beings and animals, but also towards activities (e.g., football, vacationing, etc.) and even food (e.g., ice cream, chocolate, etc.). It is a central concept to the human experience. It is also defined in terms of philosophy, psychology and religion.
It would be very difficult to explain love to a hypothetical person who had not himself or herself experienced love or being loved. In fact, to such a person love would appear to be quite strange if not outright irrational behavior.
In terms of psychology, love is seen as a "healthy behavior." "Evolutionary theories" suggest that love is a result of natural selection. From a spiritual standpoint, love is believed to be a "gift from God." Other schools of thought suggest that love is a "unexplainable mystery, very much like a mystical experience."
In Sonnet 116, Shakespeare (who wrote a great deal about love) noted:
Love is not love
Which alters when it alteration finds,
Or bends with the remover to remove.
O no, it is an ever-fixèd mark
That looks on tempests and is never shaken…
Love is a positive feeling someone feels for a person or thing. It generally provides one with a positive sense of well-being, though it can cause enormous difficulties as well. It is generally something that is wished for within human society.
Forgiveness, on the other hand, is something one offers to excuse perceived negative behavior.
Forgiveness is typically defined as the process of concluding resentment, indignation or anger as a result of a perceived offense, difference or mistake, or ceasing to demand punishment or restitution.
However, while it may be offered through a sense of love, it does not necessarily have to be connected with love at all. It can be offered as a sign of goodwill from one who may have been harmed or offended, to show that there is no lingering resentment, regret or dissatisfaction. One may forgive out of love, but it is not necessary that love be present in offering forgiveness.