In simple terms, the difference between Soft Drawn and Hard Drawn copper lies in the manufacturing process (specifically "Annealing"), rather than the material itself. Both typically use high-purity electrolytic copper.
Regarding your question about IEC 60228, Class 5 and Class 2 refer to the geometric structure of the conductor, whereas Soft/Hard drawn refers to the physical temper (hardness) of the metal. These are two different dimensions of classification.