Usually, the actual layer of material on the very outside of the entire plane is referred to as its "skin", as distinct from its "skeleton" or "structure" and in much the same sense of the words as a human's skin and skeleton. A similar word is "shell", not often used with planes (as the outer surface is very intricately connected with the structure beneath), but more often with cars and land vehicles, especially racing cars. In ships, the term is usually "hull", and this term can sometimes be used to refer to an aircraft's or (more often) spacecraft's outer layer.
The fuselage of a plane is its main body, as distinct from its wings and tail. It has both a skeleton and a skin (both mainly of aluminum, sometimes carbon fiber), as do the wings and tail. However, neither fuselage, wings or tail could be considered a plane's "outer covering".