Explaining natural selection in moth
Evolution is a change in allele frequency through time. Alleles underlying moth melanism are changing through time in response to environment change, so indeed moths are evolving.

The environmental change is induced by human activities indeed. But the question of what is the cause of the environmental change causing the selection pressure is totally irrelevant to the question of whether there is such selection pressure.

Artificial selection is in essence the exact same thing than natural selection except that there is a goal (increasing milk production or making smaller dogs for example) that is decided by humans. In the moth example, the environmental changed is caused by human activities, but it has never been a goal for human to put selection pressure on moths to force them to change color. As a consequence, change in color melanism is an evolutionary process that is induced by natural selection, selection toward a new environment.

Evolution is not just the same thing as natural selection. The reason is that other mechanism than natural selection yield to change in allele frequency. One of them is genetic drift. You can have a look to this post to have a better understanding of what genetic drift is.

Hope that helps.