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 occurs 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 scattered electromagnetic radiation.
In discussion of radiative transfer, Thomson 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 involved 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).
As the low energy limit of Compton scattering, Thomson scattering can be thought of an idealized model, very close to reality within its regime, much as classical mechanics is very close to reality within its own regime and is a limit on the more accurate relativity models. I presume that within Thomson scattering's regime, actual scattered photons do change wavelength, but the change is so small as to be negligible.