@jeaton01, this too is 100% my experience when earning my A & P licenses (Airframe and Powerplant).In my experience, a fillet is a specific type of fairing, used at the intersection of a flying surface and either another flying surface or some other part of the aircraft having an intersection with a flying surface. Fairing is a more general term, perhaps an illustration would be the bulges on Spitfire wings over the cannons. Fillets are found where the intersection is not 90 degrees, so the Spitfire has wing fillets, but the F4F and Corsair do not.
@paddy, this is a Mooney aircraft made in Texas being restored. I am not sure how a restorer's use makes it a use of 'fairing ' for British aircraft. The British Spitfire manuals use the term Wing Fillet.The wing fairing would be 100% correct in the UK so British aircraft. Personally i think both terms work well
.
https://mooneyspace.com/gallery/image/28280-wing-root-fairing/
Yet, I can see why there is confusion as both definitions have "smooth junction where two surfaces join" in their definition.
From the book, British Standard Glossary of Aeronautical Terms (revised August 1940):
TMI, as usual.