There are four different Greek words for love: agape (brotherly love), eros (sexual love), philia (friendship), and storge (compassion). The word usually used for Christian love—love for God and our fellow human beings—is agape. However, the other three words can also be applied to Christian love.
Philia
There is an interesting passage in the Gospel (John 21:15-17) when Christ asks Peter three times, “Do you love Me?” and Peter replies, “You know I love You.” In the original Greek text, the first two times Christ asks, “Agapas me?” The third time He asks, “Phileis me?” as though He is asking, “Do you really love Me?” “Do you love Me as a friend?” Philia implies a closer, more personal love than agape, and our love for God should be that of a close, personal relationship.
Storge
Compassion is a form of love that every Christian should possess. The love the Good Samaritan showed to the robbed victim was compassion (Luke 10:25-37). The love shown to the Prodigal Son was compassion (Luke 15:11-32). Compassion is what moves our hearts to forgive and be merciful, to help those in need and commands us to love our enemy. The love we have for our enemies is not philia or eros. Agape and storge are the forms of love we are to show to our enemies. We are not asked to like our enemies, to enjoy their company, to trust them. But we are to show compassion, to forgive, to be merciful, to see them as God’s children and; therefore, as brethren. It is compassion that makes charity and kindness sincere. If we help others begrudgingly or bitterly, we are not really compassionate.
Eros
Eros is usually thought of as sexual or intimate love. However, it is interesting that some Church Fathers use this word to describe the highest degree of love for God. This is because eros is the most passionate form of love—it borders on obsession. Anyone who has been in love will tell you that they can’t eat or sleep because they are in love, that the object of their love is the first thing they think of when they wake up and the last thing they think of when they go to bed, and other such things. Such should be our love for God.
St. John of Sinai (to whom the Fourth Sunday of Lent is dedicated), more famously known as St. John of the Ladder (Climacus) because of his famous work, The Ladder of Divine Ascent, says this is why so many of those saints who were once possessed by this passion of eros or its sinful counterpart, lust, ended up being those saints who most passionately loved God.
A great example of such a saint is Mary of Egypt (to whom the Fifth Sunday of Lent is dedicated), a wealthy prostitute who became one of the greatest ascetics of the Church. According to some stories about her life, she was not a prostitute for the money, since she was very wealthy, but because she enjoyed it. When she embraced Christianity, she gave up everything and lived a life of rigorous ascesis and penitence in the wilderness.
Such saints did not so much give up their passion as redirect it to God, replacing the object of their desire with God. This is a matter of great importance. Repentance is often thought of as a negative thing—as simply giving something up. But repentance is in fact positive—it is finding the right and proper object for our passions. Our passions are in fact necessary; they are a gift. Without them we risk becoming lukewarm, indifferent, something Christ declares in the Book of Revelation that He detests: “because you are lukewarm, and neither cold nor hot, I will vomit you out of My mouth” (Rev. 3:16). The saints had a burning love for God. They were the most “passionate” people of the Church, but they directed those passions correctly, set them to their proper tasks and, with singleness of heart and mind, transferred them to one object of desire—that is, to God.
~Vassilios Papavassiliou, Meditations for Great Lent: Reflections on the Triodion
