I think both are based on electrons oscillations. Can someone help me to understand?
Let's improve Krishnan's answer: A plasmon is a quantum of plasma oscillation. Thus, plasmons are collective oscillations of the free electron gas density, for example, at optical frequencies. Surface plasmons are those plasmons that are confined to surfaces and that interact strongly with light resulting in a polariton. They occur at the interface of a vacuum and material with a small positive imaginary and large negative real dielectric constant (usually a metal or doped dielectric). Phonons, on the other side, are the quanta of the modes of vibrations of elastic structures of interacting particles. If charges are involved in the particle's vibrations, you can also have plasma oscillations but, all you see is the lattice contribution to the permittivity tensor, as observed in the LO-TO phonon mode splitting in infrared experiments - not a plasmon.
Plasmons occur in metals and plasma they are modes caused due to the interaction of the material with an incident electromagnetic field( they are excitations of electrons but occur in a metal) plasmons have a characteristic frequency of oscillations similar to plasma dependent on the incident light.
Phonons are modes of vibrations (these are mainly due to thermal excitations) even though both are oscillations of electrons the dispersion as well as the source of excitation are different. For further detail you can refer Plasmonics: Fundamentals and Applications. Maier and Solid State Physics by Ashcroft Mermin
Let's improve Krishnan's answer: A plasmon is a quantum of plasma oscillation. Thus, plasmons are collective oscillations of the free electron gas density, for example, at optical frequencies. Surface plasmons are those plasmons that are confined to surfaces and that interact strongly with light resulting in a polariton. They occur at the interface of a vacuum and material with a small positive imaginary and large negative real dielectric constant (usually a metal or doped dielectric). Phonons, on the other side, are the quanta of the modes of vibrations of elastic structures of interacting particles. If charges are involved in the particle's vibrations, you can also have plasma oscillations but, all you see is the lattice contribution to the permittivity tensor, as observed in the LO-TO phonon mode splitting in infrared experiments - not a plasmon.
phonon is a quantum mechanical description of vibrational motion in which a lattice of atoms or molecules uniformly oscillates at a single frequency .
plasmons are collective oscillations of the free electron gas density.
The plasmon is a quasiparticle resulting from the quantization of plasma oscillations just as photons and phonons are quantizations of electromagnetic and mechanical vibrations
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