In my neck of the woods, when given an instruction (or, more likely, permission) to depart from anywhere but the threshhold (end) of a runway, it's given as either the taxiway intersection or another easily identifiable descriptor, i.e. "G-ICU2, cleared for takeoff from C2 on runway 15" or "cleared for takeoff midpoint runway 15".
"Short", as others have said, is almost universally used to refer to either holding before entering a runway or taxiway ("hold short") or to be prepared to not use the entire runway when landing ("land short, simultaneous intersecting runway operations in use").