Radiation hydrodynamics (RHD) is essentially "normal" hydrodynamics plus the effects of radiative transfer. When modeling a physical entity (e.g., a star or cloud), electromagnetic radiation may or may not significantly affect the result, presenting the question of whether to include the complication of radiative transfer. The momentum of photons (radiation pressure) is one factor. Much hydrodynamic code developed for astrophysics does also include effects of EMR.
Note that RHD is also sometimes used for relativistic hydrodynamics, i.e., hydrodynamics including the effects of relativity.