Elasticity: 
Whenever an external force is applied on a metal, it deforms. Elasticity is the property by virtue of which a metal regains its original shape when the external force applied on it is removed. 

Toughness: When a huge external force is applied on a metal, the metal will experience fracture. Toughness is the ability of a metal to resist fracture. The ability of a material to resist fracture due to high impact loads, is called toughness.