This is an interesting thread. Thanks.
It seems to me that the most important distinction between self-compassion and self-pity lies in the definition of compassion. Most often, compassion includes a desire to help the sufferer. Thus, self-compassion is about caring for self and wanting to do something (hopefully healthy) about suffering. Self-pity is about feeling sorry for self but having little desire and taking no effective action toward improving one's state.
Self-pity is about stagnation.
Self-compassion is about growth.