The best description of one billiard ball hitting a second billiard ball is:
Most of the kinetic energy in the first ball is transferred to the second ball.
In an elastic collision, such as the one between billiard balls, the kinetic energy is conserved, but not all of the energy from the first ball is transferred to the second ball. Some kinetic energy remains in the first ball after the collision, depending on the angle and speed of the balls before the impact.