Ductility is a property, especially of metals, of being capable to be drawn out into a wire.
Malleability is the ability to be hammered out into sheets.
A ductile and malleable material is one that can sustain large deformations beyond its elastic limit without fracture. Metals are very ductile and malleable, and may be pulled out into wires, or hammered or rolled into thin sheets without breaking. During these processes, no new compound or substance is formed. Thus ductility and malleability are physical properties.