I am making the assumption that you are talking about God's unselfish sacrificial love. The Bible speaks of that love and brotherly love and erotic love and love of country.
A passage that was just put into mind that highlights the difference between sacrificial love and brotherly love is:
John 21 :15-17
15 So when they had finished breakfast, Jesus said to Simon Peter, "Simon, son of John, do you love Me more than these?" He said to Him, "Yes, Lord; You know that I love You " He said to him, "Tend My lambs." 16 He said to him again a second time, "Simon, son of John, do you love Me?" He said to Him, "Yes, Lord; You know that I love You." He said to him, "Shepherd My sheep." 17 He said to him the third time, "Simon, son of John, do you love Me?" Peter was grieved because He said to him the third time, "Do you love Me?" And he said to Him, "Lord, You know all things; You know that I love You " Jesus said to him, "Tend My sheep. (NASB)
I am not a language scholar, but one who is once told me that Jesus kept asking Peter "Do you love me with God's sacrificial love?", and Peter kept answering with "You know that I love you with brotherly love". The reason that Peter was grieved is that he knew that the Lord was asking of him a much more difficult kind of love than Peter was then able to give. Peter, who had recently denied knowing Christ after stating that he would never do that, could not respond that he could. At least Peter recognized his failings. Christ, who knows all our hearts could still use him to build the body of believers. As Peter built that core of believers, he became capable of Agape meaning sacrificial love.
I am sure that there are other members of this site that can confirm or correct me.