You're thinking egotist.
Narcissists could give less of a shit what other people think; they love themselves just fine.
No like seriously please don't conflate the two. Humor me on this.
No please say more. As an... expert, let's say, on the issue of personality disorders, I'm highly curious to hear you explain your logic and where you got the info from. This isn't a loaded question, I'm genuinely curious. I've a lot of experience with them in person and some experience in the theory, but I'm much weaker on the theoretical aspect than the practice. Wouldn't a malignant narcissist, for example, count as someone who cares what others say? The ability to not care what people say is generally considered a result of being well-rounded, rather than a narcissism, so where does a narcissists turn into a more unhealthy form? And could you define egotist for me too? I've heard the term, but am unfamiliar.
A. I was on the path to being a narcissist, as in diagnosably so up until I found that out and made a conscious effort not to be a massive douche because I want to help people. So it might just be a personal thing, but I rather dislike being compared to Trump. That's why I say humor me.
B. Yes, a certain amount of narcissism is healthy. Self-interest is part of development, and I count myself lucky that I was narcissistic rather than depressive, as humility seems easier to learn than self-confidence.
C. So, from what I know, egotists are concerned with how people think of them and are sensitive to having their pride hurt. They are dependent on praise and admiration. Narcissists enjoy praise and admiration, obviously, but the difference is essentially pride vs. self-confidence. And mind you, it's a difference in technicalities, odds are they overlap quite frequently, and in practice both are typically douchebags. Narcissists don't care about other people, and don't really make an effort to build up relationships/their reputation, while egotists need attention and are often more manipulative. Both can be nearly sociopathic in their tendencies. Not a true expert on this, however.
@Reelya, would you say that narcissist and egotist are synonyms? Because as far as I know, they are not, even if they are very similar. From what I know, that's an egotist, not a narcissist. Ego versus Narcissus.