Let me put it in a easy way, we all know that soles has mid sole and outsole, mid sole is softer than outsole, because mid sole needs comfortability for feet while out sole needs anti-slip ability .A sole of combination of mid-sole and outsole with different density that is we call dual density shoe sole.
long long ago, there are no dual-density- outsole" saying,because most outsole manufacturers produced mid-sole and outsole separatly, but with the time goes by and technology upgrading we can produce mid-sole and outsole at once. So the mold would be a key point.