The best description of two billiard balls colliding on a billiard table is an elastic collision.
In an elastic collision, both momentum and kinetic energy are conserved. Billiard balls are designed to collide in such a way that they bounce off each other without losing energy to deformation or heat, thus making their collisions very close to elastic. Although in theory, perfect elastic collisions do not exist due to energy losses in real-world scenarios, billiard balls exhibit elastic behavior more closely than most other types of collisions.