Fae, or faerie, is the term used to describe those creatures of the Dreaming which have a pure faerie soul. Changelings are not fae, for though they have a fae soul, it is partially merged with a mortal soul.
Under this definition the Sidhe who inhabit mortal bodies are fae. This is not to say that they do not see a significant difference between their current position and their former existence.
A faerie consists in essence of two elements: a faerie soul and a dreamstuff form.