The bounce in mechanics is defined by the coefficient of restitution, which is how elastic something is. Technically it's related to the energy lost in the collision.

Perfectly elastic objects bounce apart with mirrored velocities. No energy is lost.

Perfectly inelastic objects just stop. All of the energy is dissipated through noise, heat, and deformation.

Momentum is conserved in both.

For drivers ed, cars are almost perfectly inelastic.