What is the difference between hammer efficiency and coefficient of restitution?

Hammer efficiency refers to the ratio of kinetic energy of the hammer to the rated energy (or potential energy). In essence, it is undoubtedly that certain energy losses are induced by the hammer itself prior to the actual impact on the driven piles. For instance, these losses may include the misalignment of the hammer, energy losses due to guiding friction, inaccurate dropping height etc

Coefficient of restitution refers to a value indicating the strain energy during collision regained after the bodies reverting back to their original shapes. If the coefficient of restitution is equal to unity, it means that the collision is elastic and all energy has been returned after the impact action. Hence, this is an index showing the degree the impact action in terms of elasticity.

In mathematical forms,
Coefficient of restitution = -(v₁-v₂)/ (u₁-u₂)
where
u=initial velocity
v=final velocity after impact

This question is taken from book named – A Self Learning Manual – Mastering Different Fields of Civil Engineering Works (VC-Q-A-Method) by Vincent T. H. CHU.