When I hear "Total War," I have images of indiscrimant, or at least wholesale slaughter of civilians and defenders, as well as condoned rape and atrocities versus individuals.
Well if you include the concept of an economy totally geared towards a war effort, the above is what I understand by total war too.

But I don't get a clear image of hard war. It may sound a bit sarcastic, but what is the difference between hard war and a scorged earth strategy?

And how does it differ from medieval warfare? i.e. destroy supply routes to the enemy, and lay in the mud and hope that they die of starvation before you do?