Thomson Scattering is a type of scattering of photons by free charged particles (e.g., electrons) in which the outgoing photon has the same Frequency/Wavelength as the incoming photon, i.e., a type of Elastic Scattering. It happens when the photon energy is much less than the mass energy of the particle, and is the low-energy limit of Compton Scattering. It tends to polarize the Electromagnetic Radiation.
In discussion of Radiative Transfer, Thompson scattering and the higher-energy analog, Compton scattering are referred to as Electron Scattering, because an electron's direction is changed, i.e.,it is scattered, and/or because it causes a photon's direction to change, i.e., it scatters the photon.
Thomson scattering is an element in the physics of stars. Similarly, it affected the Cosmic Microwave Background as a polarizing influence when the electron density of the universe was high enough to significantly scatter the photons (i.e., before and during the Epoch of Reionization).
Baryon Acoustic Oscillations (BAO)
Thomson Optical Depth