The idea of self love in the often used sense is to believe in yourself, not talk bad at or about yourself and do nice things to yourself that make you feel well.
The other one is called narcissism, yes. It stems from a bad self image which subconsciously gets compensated through grandeur, selfishness and other things that you can read from the dsm or icd. Basic clinical psychology. The roots of that bad self image can be a bad childhood, brain damage or abuse amongst other things.
As someone who has pretty large trove of experience there: in relationships, the stuff that is good for one and bad for the other is wrong. Only good and acceptable are viable combinations.