The smallest unit of sound wave energy is the phonon. The phonon and the photon and the electron can in some ways all behave like a small particle.

Basic Answer:

The terms "electron-phonon interaction" and "phonon-electron interaction" mean the same thing and one almost always hears the former and not the latter. In a nutshell the term refers to the fact that the usual idea of separating the quantum system of electrons and the quantum system of vibrations (phonons) is an approximation that does not answer questions about the exchange of energy between the two systems. The next most sophisticated treatment involves including a term in the Hamiltonian that approximates the mechanism for that energy exchange. That term is called the electron-phonon interaction term.

Addendum on Electron-Phonon Interaction:

If the question were posed asking to explain the electron-phonon interaction, this answer would have to discuss the process of calculating electronic energies for fixed nuclei and then solving the problem where the nuclei are allowed to move within the adiabatic approximation. That leads to the two quantum systems mentioned above and thus to the need for an improvement which treats electrons and nuclei both being treated at the same time in a quantum mechanical fashion. One proceeds with an electronic Hamiltonian and a nuclear coordinate Hamiltonian and adds a third term called the electron-phonon interaction which is meant to be a good approximation to the full quantum system and is amenable to reasonable approximation methods.

A phonon is a collective vibrational mode in an ideal crystalline solid.

A single phonon is pure vibrational mode. It is direct analogy to a pure vibrational mode in a musical instrument such as a string of a guitar.

It can be said that it is a sound wave, but the vibrations allowed that are pure single mode vibrations are more extensive than simple sound waves.

Phonons, in their original and normal sense, occur in perfect crystalline structures where each atom has a specific equilibrium location that is repeated regularly in space.

In a pure single phonon mode there is a periodic vibration (i.e. displacement) of each atom that is described as a sinusoidal variation in space and time. One specifies a particular phonon with a wavelength, direction and frequency, just as with a sound wave.

In real solids, there are imperfections, but they are near enough to idea that the idealized concept of a phonon is usually completely adequate.

Finally, phonons can be described as classical vibrations as is natural in classical mechanics and they can be described as quantum vibrations using quantum mechanics. The quantum description is fundamentally correct, but the classical description is very useful and convenient in many cases. Some people would say that you should not call the collective vibrations of a solid phonons unless you are describing them as a quantum phenomena but other people would say that is too picky. Usually, however, the term phonon implies that quantum nature of the vibration of a crystal.

sound and other mechanical vibrations are quantized as bosonic particles called phonons.