Scales are secreted from follicles that are linear rather than spotted. The similarities between scale excretion and feather secretion are far more striking than the differences. Your characterization is simply inaccurate. That both feathers and scales are molted is far more meaningful than that their molting processes vary. Before feathers arose, hair follicles had already evolved in some skin regions.
Hair cells are also a type of skin cell.
In the embryo, skin cells are all the same type, but some will develop into hair cells, others into scale-producing cells, others into basic connective cells. There are chemical processes unique to the mature cell types, as well as shapes and sizes. Before feathers, true follicles were largely unique to hair cells. Because hair and scale cell types exist in proximity to each other and because they share a common regulatory cascade, it is possible, even likely, that genes expressed only in hair follicles become inadvertantly expressed in other skin cells. This could arise either by mutation or by an environmental insult like a toxin or a temperature extreme.