Well, those who distinguish the two do so on the basis of "natural selection" describing the process of being more fit for survival in an environment and so hav

Well, those who distinguish the two do so on the basis of "natural selection" describing the process of being more fit for survival in an environment and so having more offspring survive compared to competitors, vs being able to out-compete in providing more offspring in the first place. So, yeah, having more surviving progeny by means of social dominance (sexual selection) can be considered a form of natural selection, but it's through internal rather than external forces. It's a useful distinction.