A distinction is commonly made between a ball (solid) and a sphere (the boundary of a ball). This distinction is made in other dimensions as well (e.g. circle versus disc, in 2D).
From what I've seen trying to research this online, the word "cube" is usually used to refer to the soild. Is there any standard name for just the boundary of a cube? The only thing that came to mind was "box" but that both doesn't seem to be a standard term, and might intuitively refer to the boundary of any rectangular prism.
(My question extends to squares as well, i.e. is there a standard name for just the boundary of a square? And a similar question could be asked in reverse about the torus, where that name is usual used to refer to only the boundary.)
If there is no standard name, my follow-up question would be: why do we have distinct names for spheres and balls, but not other common solids? Just historical accident? (Is the distinction made in languages other than English?)
I know of no standard names for those boundaries.
Mathematicians give the sphere and ball those distinctive names because they often want to discuss both in the same context.
The boundary of the cube comes up less often. In some contexts it's the two skeleton. The one skeleton is the set of edges.
To refer to a torus together with its interior you would say "solid torus".