Ductility is the measure of a material's strength under tensile stress (i.e. being stretched). Malleability is a measure of the strength of a material under compressive stress (i.e. being hammered).

ductility and malleability are properties of metals. ductility is how well it conducts electricity or heat, and malleability is the ability to be moulded into shapes. metals are moulded at very high temperatures.