One definition of a 'shoulder' is something which projects, like a human shoulder, to the side of an object. (Bottles and tools can have 'shoulders'). So that includes the strip alongside the edge of a road, whether it's surfaced or not. However the shoulder of a motorway is always surfaced, making it a hard shoulder.
Interestingly, the M90 ( Forth Road Bridge to Perth) was built on the cheap with no hard shoulder. Following a horrendous night-time accident involving a broken-down truck and a car full of people, it was officially stated that the accident would not have occurred if a hard shoulder had been in place. So several miles of hard shoulder were built, each mile costing the same as a mile of the original motorway. There are still long stretches of the M90 with no hard shoulder, and occasional emergency lay-bys only.
Some other roads had shoulders which weren't metalled. The term 'hard' explained that shoulders on the motorway were as solid as the rest of the carriageways.
I always thought that if a road did NOT have certain things such as hard shoulders. emergency phones etc it could not be classified as a motorway. So a motorway without a hard shoulder should be the A-whatever.
i believe that in road construction, there is also a 'soft shoulder' - a roadside which is simply earth, and thus distinguished from a 'hard shoulder' which is a solid surface, usually tarmac.