Natural Selection... as opposed to... what, exactly?
As opposed to all the OTHER types of selection out there.
Artificial selection was separated from natural selection in the beginning specifically to allow Darwin and others to say "You accept that humans can do this sort of thing. If we can do it, Nature can as well--so if you accept artificial selection, you must accept natural selection as equally valid." Yeah, it's all natural, but from a rhetorical standpoint dividing the two was effective.
Sexual selection is distinct because natural selection tends to increase fitness, while sexual selection can basically do whatever it wants. A lot of organisms have things that make no sense from the perspective of increasing fitness to the local environment, such as bright colors on otherwise drab birds, bright spots on fish, elaborate dances, and the iconic peacock tail. The reason? Women find them sexy. Understanding the role of "Hey, that's kinda hot" in evolution was a major advancement, and warrants a unique term to guide our thoughts on the topic by reminding us that sexually reproductive organisms may have unique issues.
Genetic drift isn't actually selection at all, but rather random shifts in allel frequency due to statistical phenomena. I shouldn't have to point out the advancements that were made once this was discovered.
Ontogenetic issues are coming to light now as well. We've been extremely hesitant to address these factors, particularly pre-birth/hatching factors, because of some mistakes researchers made in the past; evo-devo is, however, starting to show that a rather enormous portion of selection occurs before the organism ever draws breath.
Then there are aspects of organisms that aren't selected for at all, but exist due to structural or historical considerations--for example, our four-limb bauplan isn't due to any sort of selection, it just happened that the lobe-finned fishes that we evolved from had four limbs. For more on this, look into the history of fingers and toes. Or some rather....strange.....research on adding weighted "tails" to chickens that came out recently. (I am not even slightly joking here; someone put clay cones with sticks in them on the back ends of chickens to see how they walk, FOR SCIENCE!
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Then there's just plain old fashioned bad luck. I don't care what your genes are, you get hit with a 10 km rock falling from space you--and probably all of your population, if not species--don't get to pass your genes on to the next generation. It has nothing to do with fitness for an environment; it's just (from the perspective of evolution and the biosphere) pure random chance who gets to live and who becomes part of a fireball that hit three states.
There are others I'm forgetting off-hand (the kid had a nightmare and I was up half the night with him, so my brain is't at peak efficiency). My point is, there are a myriad of selective processes that we've identified. Natural selection, properly understood, is one of them.
You're stripping the phrase "natural selection" from its historical context and looking only at the vernacular use of the words in the phrase--both of which are unwarranted when dealing with highly technical jargon (and yes, "natural selection" IS highly technical jargon). The phrase doesn't mean "selection that is natural"; you can't break it into its constituent parts and figure out what it means that way. Rather, the phrase means the suite of selection processes that the organism is subject to. Typically this excludes human factors, but that's because human factors we have more control over (ie, we can stop shooting rattlesnakes but we have a harder time addressing rainfall).
