Right. Selection is selection. Humans select for traits that we deem desirable. Nature selects purely for survival. The criteria are different, but still, the individuals thus culled to breed the next generation are ever-so-slightly different from the general population, and pass on their qualities to their offspring. The result is a gradual change in the species (how gradual depends on the intensity of the selection pressure), with each generation being a tiny transitional link in the chain of descent. If evolution were impossible, then humans couldn't do what this group has so easily done with foxes.
Another striking example is tusk size of the African elephant. About 80 years ago was a busy time in the ivory trade. The elephants with the biggest tusks were the first to go. As a result, almost none of the modern elephants have tusks that reach the huge sizes of those in years past.
The "big tuskers" sported a feature specifically detrimental to survival, were selected against, and the elephants of today reflect the bias towards smaller tusks.
Like you said, selection is selection.