Hi AppleScratch and welcome...
I see why it makes discussion easier to have the distinction, I just can't get to any actual basis for it that is consistent, and it becomes interesting to ponder.
Biological systems rarely have clear cut distinctions unless there is some quantitative value by which to distinguish them. So a group of plants with leaves between 2 cm and 5 cm long belong to this species and those with leaves 7 cm to 10 cm belong to another species. There is something we can quantify and measure to assign a distinction. As you can see by the examples you are pondering, the distinction between "natural" and "artificial" selection is not something that can be quantified and so it becomes difficult to nail it down into distinct categories.
As an example, white-tailed deer use their antlers to fight for the right to mate, so those with bigger, stronger racks have better chances to produce offspring, so we would say natural selection favors larger racks. However, hunters tend to shoot those deer with bigger racks, and since we could consider hunters to simply be apex predators, we could also say that natural selection also works against large racks. But, the way hunting seasons are typically scheduled, the mating begins before or very early in the hunting season and even though a particular male may get shot during the season, he may have already impregnated several females.
The confusion comes in because the predator in question is humans, which makes one think that the selection is "artificial." But if you consider that humans are just a predator in a predator / prey relationship, it is pretty much a natural selection system. However (there's that word again that indicates how difficult it is to define distinct categories), selecting an individual based on antler size is hardly a "natural" choice. Deer with large antlers are typically older, wiser, stronger and warier than their younger, smaller racked comrades. Thus selection for rack size is not a choice based on what makes the animal suitable or preferable prey, but on some arbitrary human preference.
So I would suggest that artificial selection is selection that favors or enhances a particular trait regardless of it's potential effect on fitness. These traits are selected for because of their benefit to humans, not because of their benefit to the organism undergoing selection (even though they may, in fact, improve the organisms ability to survive).
I hope this helps some.
HBD
Whoever calls me ignorant shares my own opinion. Sorrowfully and tacitly I recognize my ignorance, when I consider how much I lack of what my mind in its craving for knowledge is sighing for... I console myself with the consideration that this belongs to our common nature. - Francesco Petrarca
"Nothing is easier than to persuade people who want to be persuaded and already believe." - another Petrarca gem.
Ignorance is a most formidable opponent rivaled only by arrogance; but when the two join forces, one is all but invincible.