As someone with an interest in folklore, though by no means an education in its study, I find that oftentimes the idea in popular culture of "The Fae" seems very loose, almost to the point of being unhelpful.

Where does the idea of things like sidhe, elves, brownies, pixies, piskies, puca, selkies, etc as a unified category of beings nebulously identified as "The Fae" come from?

And what caused certain traits to become attached to this category, like their supposed vulnerability to iron, love of stealing names, and habit of replacing people with changelings?

These all seem to be very common traits of their modern depictions and appear in such media as The Dresden Files, The Ancient Magus Bride, Changeling the Dreaming/Changeling the Lost, and can also be seen in a variety of online posts about the subject.