Question

how photons and phonons are they differ?

Answer 1

Photons are light quanta; they're the units of energy that a wave of light can deliver. Phonons are so-called quasi-particles in that they're purely fictional. When a wave travels through a solid (like a sound wave) that wave can also be described as phonons of a specific frequency. In that sense, photons and phonons are very similar but where photons are an actual physical phenomenon, phonons are simply a mathematical aid to make solid state physics more understandable.

Answer 2

Photons are the particles of Electromagnetic field, meaning that they are the quantisation of the EM vibrations. Phonons on the other hand are quasi-particles, and result from the collective excitations of atoms in solid materials. In other words they are the quantisation of atomic vibrations within the lattice of a solid crystal. Sound waves in solid materials are phonons, which is where the term phonon comes from the Greek "phone" (meaning sound) and "on" which is the physicists term for particle. Phonons though can have transverse or longitudinal modes of vibration, whereas photons in EM waves only exhibit transverse modes.