Consider a system of two bodies. The system is a closed system which implies that no external force acts on it. The system may consist of two balls or two springs or one ball and one spring and so on. When two bodies interact, it is termed as collision. There are no external forces acting on the system.
Let there be a head-on or central collision. In such collisions, colliding bodies move along the line joining their centres. The collisions are of two kinds :
Perfectly Elastic Collision
If the forces of interaction between the two bodies are conservative, the total kinetic energy is conserved i.e. the total kinetic energy before collision is same as that after the collision. Such collisions are termed as completely elastic collisions.
Perfectly Inelastic collision
When two colliding bodies stick together after the collision and move as one single unit, it is termed as perfectly inelastic collision. It is like motion of a bullet embedded in a target.
The momentum is conserved in all types of collisions. But kinetic energy is conserved in elastic collisions only.