How could genetic drift explain differences in genotype frequencies among populations?

If a population experiences a form of genetic drift, then their genome/genetic code would change. This then can cause the frequency to follow as well. Best example I can think of right now is moths in the Industrial Revolution: all of the soot released into the air caused the moths to be easily seen by birds that ate them (they were all white). This then caused those that were darker, like dark brown to match its new surroundings, weren't eaten by the birds because they could blend in. This caused the phenotype frequency (and therefore genotype) to change to having dark moths being more common than light. And we still see that today! Most moths are still dark brown.