There are 3 Types of Collisions Elastic, Inelastic and Totally Inelastic collision. Momentum is conserved in all these three types ( No external force is involved, so the system is called a Closed System. ).
When a Bat hits, a Ball Momentum is changed because Bat provides an external force. But when the Two Balls Collide the forces are Internal and hence the Interaction of the Balls due to Internal Forces does not change the Momentum of the "Closed" System. Momentum is not lost in Closed Systems.
Elastic Collision
In an elastic collision, there is neither loss of kinetic energy nor loss of Momentum. Therefore it is assumed that such experiments are conducted on frictionless Smooth surface so that the loss of Momentum due to an external force such as friction does not happen.
Inelastic Collision
In an Inelastic collision, there is some loss of Kinetic Energy ( In Real life these collisions are Generally familiar) but no loss of Momentum. Energy is lost in Heat and Sound.
Completely Inelastic Collision
1. There is loss of Kinetic energy during the collision and also the two objects stick with each other.
2. There is no Bouncing off.
While doing numerical on one should carefully read the question to infer what's happening during the collision. Following should be understood from the given numerical:-
1. There is Bouncing or Not. Bouncing Indicates that the Collision is Inelastic or Elastic. ( So in the question, you would see the words "Balls Bounce Back."
2. Inelastic Collisions don't have any Bouncing.
3. an External force is present or not. This is because in Collisions of any Type Momentum is Generally Conserved. For Momentum to stay, conserved External Force has to be absent. The system must be closed system/