I'll explain the difference between forgiveness and love and it comes down to this - basically forgiveness is about you, but love is about the other person.
Example.
Suppose a thief steals your car, will you forgive the thief because the thief is a nice person? because the thief is good-looking? No. Forgiveness is entirely about how good you are, not about how good they are.
But suppose you see a person in need on the street, you might love that person by giving them food, because you think they are a good person in need of food. Would you give money to a homeless person if you knew they were the person that stole your car? No, no sensible person would give money to a person they thought is not worthy of it. Now love is not entirely about you but more about how good the other person is. That's why people give their spouses $200 gifts at Christmas but give only $10 to the homeless person on the street. Because the love a person has for their spouse is greater than the love they have for a homeless stranger. In other words, a person sees their spouse as more worthy than a stranger on the street.
Love and forgiveness can be seen as two separate things. For example,
God sending His son to die on the cross for our sins is an act of love because God saw the worth of humanity as being created in His image. If we were merely animals or demons, God would not have sent his son to die on the cross for us.
God forgiving our sins is because of His mercy (entirely because of who He is, His goodness and kindness), not because of who we are.
So love is partly about the person being shown love. But forgiveness is entirely about the person doing the forgiving.
If you do an online Bible word search for the words love and forgive in the KJV, the only verse where love and forgiveness appear together are and this is about love as a response to being forgiven, not forgiveness as an example of love.
The Bible often puts mercy and forgiveness together e.g. and
http://ebible.com/query?utf=8✓&quer...e=http://www.talkjesus.com/pages.php?pageid=1, and this is resulting from God's goodness or kindness (). Therefore forgiveness is not really an example of love, f
orgiveness is an example of mercy, which comes from God's goodness and kindness.
To give an example. Suppose a thief is standing before a judge. The judge pardons the thief or reduces the sentence not because he loves the thief, but because he is merciful. The judge may actually hate the thief because he is a thief, but shows mercy because the judge is good and kind. So the main difference between goodness/kindness, mercy and forgiveness, and love, is that love implies some worth or quality in the offender, but mercy and forgiveness is entirely because of who the pardoner is. The story of the good Samaritan is about love, because the good Samaritan saw some worth in the person he helped. But a story about forgiveness is about the noble qualities of the forgiving one, not the forgiven one.
But suppose you do something good to those who offended you, then d
oing good is a kind of love (http://ebible.com/query?utf=8✓&quer...e=http://www.talkjesus.com/pages.php?pageid=1), and this could be because you see some worth in the person as a human being. But this is not forgiveness, as forgiveness is of the heart, and forgiveness requires no actions.
So when you forgive someone, you are being merciful to them, and you can forgive someone without loving them. But if you do something good outwardly for those who hurt you, then you are showing love. On the one hand Jesus says to forgive, and on the other hand Jesus says to do good. In other words, Jesus is saying to show mercy (by forgiveness) and show love( by doing good). The mercy is about not doing something negative (not to take revenge, not to punish etc) and showing love is about doing something positive. The mercy and forgiveness normally involves no outward action (just an act of the heart, with a decision not to do something), but the loving and doing good involves action (both of the heart and outward).