A plasma, consisting of neutral particles, ions, and unbound electrons, responds to the oscillating electric field of incident electromagnetic radiation primarily through the motion of electrons (ions and neutral particles can often be regarded as stationary due to their larger mass). If the frequency of the incident radiation is sufficiently low and the plasma frequency is sufficiently high (corresponding to the Rayleigh scattering regime), the electrons will travel until the plasma object becomes polarized, counteracting the incident electric field and preventing further movement until the incident field reverses direction. If the frequency of the incident radiation is sufficiently high and the plasma frequency is sufficiently low (corresponding to the Thomson scattering regime), electrons will only travel a short distance before the electric field reverses direction, making collisions with other particles unlikely during a given oscillation.
If the frequency on the incident radiation is intermediate and a high density of neutral particles and ions is present, electrons will travel far enough to collide many times with other particles but not far enough to significantly polarize the plasma object. This characterizes the collisional scattering regime. The linear oscillation of unbound electrons in a relatively-small space gives rise to a short-dipole radiation pattern.
This is analogous to a spring-mass-damper system, where the polarization of the plasma object creates the restoring force and the drag due to collisions with other particles creates the damping force. The phase shift of the scattered wave is 90º in the Shneider-Miles regime due to the drag force being dominant.
Note that, in this context, Rayleigh scattering is regarded as  volumetric small particle scattering rather than an even broader short-dipole approximation of the radiation. Otherwise, Thomson scattering would fall under the banner of "Rayleigh". Mie scattering experiences a similar ambiguity.