Selfishness is caring for yourself because it is yourself. Self-care is caring for self because you have the greatest influence to do so.
Selfishness is loving yourself first, putting yourself before others. Self-care is loving others equally with yourself.
Selfishness will inevitably harm others. Self-care does not harm others if at all possible.
In selfishness the self is above others, in self-care the self is equal to others.