A push or a pull on an object is a force. 

A collision occurs when two or more things come together to make an impact. 

 Deformation takes place when something changes shape( temporarily or permanently).

If an object has a permanent shape change, it has damage.

Energy in motion is Kinetic Energy.

All objects do change shape when they are pushed in a collision.

Mass is how much matter is in an object.

The distance an object moves in a given amount of time is speed.

How much you have to push on an object to get it to deform depends on the breaking point and the elastic limit.