That's not really a distinction. Kin selection is a phenomena by which genes can propagate despite them not benefiting (or even harming) the individual that possesses them if it increases the probability of reproduction for other individuals possessing the gene (eg. if they are likely to be related).

It's evolutionarily plausible and explains a massive range of traits and behaviors up through full altruism. See eg. "gay uncle" hypothesis: https://en.wikipedia.org/wiki/Biology_and_sexual_orientation...

I would describe kin selection as a phenomena that is caused by natural selection because natural selection is a phenomena describing propagation of genes and not propagation of individuals. This is a subtle point and often not taught unless taking specific relevant coursework (I learned about it in an animal behavior class).

I am likely using slightly incorrect phrasing and evolutionary science experts may phrase things differently, though I am confident in the essence of this argument.

> Natural selection is by the environment, kin selection is by the organism.

This is simply a false statement. Kin selection isn't distinct from natural selection. Kin selection is the idea that a trait could be harmful to an organism but if it confers sufficient benefit to close relatives (who are likely to have the same gene), the trait can be favored. It is one of the core ideas of "the selfish gene" view -- that from an organisms vantage point such a trait should go extinct, but viewed from the gene's vantage point, it is a desirable trait.