What is the relationship between sexual and natural selection?
You're not wrong, per se, but in practice they refer to two different concepts.  I honestly think the Wikipedia article does a good job, in particular this sentence:


  In summary, while natural selection results from the struggle to survive, sexual selection emerges from the struggle to reproduce.


It also cites Darwin:


  The sexual struggle is of two kinds; in the one it is between individuals of the same sex, generally the males, in order to drive away or kill their rivals, the females remaining passive; whilst in the other, the struggle is likewise between the individuals of the same sex, in order to excite or charm those of the opposite sex, generally the females, which no longer remain passive, but select the more agreeable partners.


The whole argument is moot when dealing with individuals that aren't reproducing sexually, of course.