Loving kindness and compassion both originate in the heart. Both evoke a warm, fuzzy feeling. And each tends to be confused for the other, and vice versa.
Loving kindness, or metta, or unconditional love is the practice of generating love in one's heart towards all people, regardless of how lovable they are.
Far enemy: hate
Near enemy: attachment
Compassion, or karuna, arises when we feel sorry with someone. We feel their suffering. It starts with feeling compassion for our own suffering, the unsatisfactoriness of one's own life.
Far enemy: cruelty
Near enemy: pity (feeling sorry for the other person)
While different, I find those two inclinations of the heart to be intimately related. Loving kindness practice naturally leads towards feeling compassion, and compassion for self and others facilitates the openness of the heart needed to feel loving kindness.