Nothing to do with temperature, it's all in how it is created.
Hard ice is what comes put of most people refrigerators. It is ice that is frozen form the outside in, expansion is limited so the internal part when it freezes it is under pressure. Your home fridge does this. That's the white part you see inside the ice cube. It's denser and harder then the clear part on the outside.
Commercial ice production (like in a drink machine) is made with falling water. The water is recirculated and continuously cascades down a grid wich is cooled below freezing. Slowly the water freezes onto the grid and fills in the holes. Since the ice cube only freezes from one side it is not forced into solidifying under compression. Thus the term, soft ice. Then they momentarily reverse the freeze section and warm the grid, the ice pops out and that is the crash sound you occasionally hear.
But it is all water frozen at (generically) 32?
Blocks of ice will last longer but not get the surrounding medium as cold as smaller pieces of ice.