Loving and caring goes together. You can't fully love someone unless you care for him or her. If your spouse says he or she loves you but is totally indifferent to your happiness or well being, then you probably will not appreciate that love very much. Yes, it is possible to love and not show any care. This form of love is very immature. As an illustration, picture a spoilt wife who loves being treated like a princess. She truly loves her husband, but puts her own comfort and well being above every one else's.
A better expression of love is showing care at the same time. Continuing with the illustration above, picture a wife that cares if her husband is unhappy or unwell. She feels sad when her husband is sad. But if she does nothing other than feeling sad or sorry, it is love with concern, but devoid of action.
Moving along next, we have love that is coupled with care and action. A loving and devoted wife not only cares but makes sacrifices for her husband's happiness. By sacrifices, I mean doing things that require time or effort, or simply making way for the other person. This is the way that God loves us. John 3:16 says "For God so loved the world that He gave His only begotten son, so that whosoever believes in Him should not perish but have everlasting life." God doesn't only loves us. He doesn't only cares for us and does nothing. He loves us, and He sacrificed His only begotten son, so that we may have everlasting life. Love is followed by action, so that the object of His love benefits. That is the way He loves.
In Mark 12:31, Jesus said, the second greatest commandment is "Love your neighbour as yourself." I don't think this verse is exhorting us to simply develop a feeling of love for our neighbour. True love requires a sacrifice that result in someone else's benefit. Not necessarily big sacrifices all the time, but nonetheless giving up of something that is of importance to yourself. The ultimate love calls for the ultimate sacrifice. John 15:13 says "Greater love has no one than this, that he lay down his life for his friends." That's Christ's love.