What is your defination of Love ??

I think that when discussing love in English it is good to bring in the four Greek words for love; agape, eros, philia, and storge. This allows us to discuss the subject with more precision. In English the word is not so precise as we can say I love pizza and I love you.
Greek words for love:
Greek words for love - Wikipedia, the free encyclopedia

To answer your first question; God is love.

Does the meaning differ according to relationships?

In my personal opinion, yes and no. I would say, yes, because it is expressed differently according to whom it is that we are loving, mother, father, sister, brother, daughter, son, friend, God, etc... However, I understand that all expressions of love share fundamental roots. These roots, if you will, Aristotle would argue and I would agree, are ethical and for the good. If I recall correctly, Aristotle makes four distinctions of 'friendships' and they differ by degrees of intimacy but the wisdom is applicable to love. The idea is that we desire the absolute goodness, beauty etc... and we see or find these in a finite being. I would recommend that you read Nicomachean Ethics by Aristotle: Aristotle: Nicomachean Ethics

I think it is Aristotle who argues that the superior love and the cause of true love is a love for the 'good' and we see the goodness in the beloved and it inspires us to love him/her in whom we behold or who brings out within us this absolute ethical/beauty. This may be in Nicomachean Ethics. There is also the love that comes with duty; such as that of a parent, and other types (?) of love etc... The ultimate love, of course, is the love of God. God being love itself is the root of the love we experience in a variety of ways with different people and in different occassions. To love love itself! What more can I say? Song of Songs provides a mystical reading of that love. Someone once said: Our hearts are restless until they rest in Thee - meaning - God.

Hope this helps. :p