The difference between "selfish" and "self-centered" actually lies in the intensity or the person who is in front of you. I mean, "selfish" is kind of a 'cheap' word which you can easily use in front of your friends. Well, if you are in a reputed or good place and among elders , I would suggest you to use the word "self-centered" because that sounds good and in a way, it makes you look a man with etiquettes. Nonetheless, both the words have more or less the same meaning.