H13 is a hot work die steel, which is a steel formed by adding alloying elements to carbon steel. It can be used in aluminum alloy die-casting molds, hot extrusion dies, and forging press dies. H13 steel also is called 1.2344 steel.
D2 is tool steel and its content of carbon is 1.5%, the chromium content is 11.5%. The hardness will up to 60HRC by heat treatment. It also can be called DIN 1.2379 steel. DIN 1.2379 steel has good wear resistance and toughness. But its corrosion resistance is not good.