When it’s used alone (without reference to mutations) I take “natural selection” to mean what Darwin meant by it.
As scientists often do, Darwin resorted to accounting for the natural world in terms of the technology of his time. He grew up in the heyday of the technology of breeding, when most of our breeds of livestock were being created. From that technology he adopted a set of assumptions. First, you can look at differences between creatures in a species as consisting of certain ways they vary. Second, the ways they vary are inherited. Third, human breeders can identify and select for breeding those creatures that come with particular variations, resulting in those variations becoming more common in future generations.
In the natural world most creatures born in each generation die else populations would increase out of control. In effect there’s a process of selection going on. Darwin concluded that, among the variations a creature comes with, some are bound to affect whether or not it gets “selected” to leave progeny. Identifying this process with how breeders selected for specific variations, Darwin called it “natural selection.”
“Some of the ways creatures vary will affect which ones get to leave progeny.” If you believe creatures vary only in specific ways, as people did then, then that was a truism. What was to impress people in “The Origin of Species” was Darwin tying this principle to another principle: evolution equals adaptation: creatures evolve by becoming more adapted to their environment. The variations nature selected for, Darwin concluded, were those that made creatures better adapted to their environments. As variations for improved adaptation became concentrated in later generations--through natural selection--new species better adapted to their environments would automatically emerge. A theory of evolution was born.
I’ve several problems with this principle. First, adaptation could as logically be the result of the process of evolution, as its cause. Whatever the mechanism driving evolution is, it will almost inevitably make creatures better adapted over time. Then you’d say, whatever drives evolution is what makes creatures more adapted. Turning that around, as Darwin did, claiming that whatever makes creatures better adapted must be what drives evolution, was faulty logic.
Also faulty logic was his claim that what makes creatures more likely to breed are variations that make them better adapted to their environment. Any process of selection is a set of conditions; what gets selected is whatever best satisfies those conditions. What gets selected in natural selection is not necessarily greater adaptation, it’s what satisfies the particular conditions natural selection puts living creatures through. These are: surviving competition for scarce resources to reach sexual maturity; generating as many copies of oneself carrying one’s characteristics as possible; seeing those copies survive to pass those characteristics on in the next generation. Prominent among characteristics helping creatures meet those conditions will be aggressiveness and deceit to meet competition for scarce resources, seductiveness and rape to generate as many copies of one’s characteristic as possible, and murder of other creatures’ progeny while defending one’s own. Because those characteristics best satisfy the conditions set by natural selection, those are the characteristics it would concentrate in succeeding generations. That, logically, must be the main effect of natural selection.
It's true, being better adapted to the environment could help a creature meet one or two of those conditions. But I doubt if it would contribute nearly as much. Resources directed to mere fitness will satisfy the conditions set by natural selection less directly than those others allocated to the other characteristics I listed.
Now we can test the theory of natural selection. Do evolved creatures show primarily the characteristics its conditions select for? And I’d say, apart from fitness, no. We, for example, are not marked primarily by aggression to our fellows, deceit in mating, and lethal nepotism. Therefore the theory of natural selection fails the test.
After Darwin’s death the theory of natural selection fell out of favor for yet another reason: experience showed it wasn’t true. Imagine living creatures having been acted on by natural selection for millions of years--there'd be very little variation left among them. Yet before they began applying artificial selection to wild species breeders found them to carry abundant variation. Was that because variation was continuously being created? No. Once the breeders had selected in wild species for exactly the set of variations they wanted, no new variations appeared. Variation in wild species was clearly not undergoing a process of selection anything like artificial selection.
Today natural selection makes less sense anyway. We're losing the sense of living creatures differing from one another in terms of specific variations. Few genes correspond to single characteristics. We know creatures vary more as wholes than as bundles of individual characteristics. So there aren't specific ways of varying for natural selection to identify individually and select among.
Natural selection fell out of favor in the late 19th century. Not until the second half of the 20th century did it become associated with genetic mutation and win broad acceptance.