Love as it is defined in the West is usually concerned with attachment, "I'll like you if you like me." "I'll love you if you agree to be mine." There are also deeper things in that love, but they also include attachment.
Lovingkindness tries to be more unconditional. It's usually defined more as "unconditional love". This is wishing another person well whether they are connected to us or not, whether they like us or not, whether they agree to be "ours" or not. It's just an unselfish wish, without so much of "me" in the way. Whereas "Love" in the West may include that, but many people there would find it very difficult to get to that. It also includes all this attachment and conditional love, where, "If you say and do as I want you to do, then I'll love you", "You're there to make me feel good," and if you don't, then, "I don't love you any more."
If we can take this attached type of love, and use it wisely, we can start to develop more unselfishness in our relationships, so that another person's development doesn't come as a threat to us. Because usually, as love is defined in the West, we want to be "number one" in the other person's eyes, and we want them to find happiness in us, and be the most important thing in their life. But, how can that be so? That is happiness dependent on someone else. As we develop, we understand we can't expect that of another person, because this type of happiness brings with it possibility of Dukkha.
So we try to develop more Compassion in our relationships, more Lovingkindness and unconditional love. We want our loved ones to develop, which means they're going to need us less. However, we don't see that as a threat, because as we see them develop we realize that they can help us on another level that is wonderful. So we become spiritual friends walking along the Path, developing the Paramis together.