.. probably a very misunderstood term. A building made of concrete and rebar is a composite structure while those made of steel sections are not. Which is stronger and better? They both have different properties, availability of materials and pose different challenges in construction and design.
As for aircraft, technically as soon as you introduce the use of fiberglass and resin(edit: or duct tape, packing tape if so inclined, thanks Jack!) it can be considered composite even if just for sheeting. I think this is where the term "fully composite" came about to help differentiate a full fiberglass fuselage and wing from say something that is glassed balsa. Glider guys will often classify by components, so something like "composite fuselage with obeechi sheeted wings vs fully composite", for example.