The radiation belts of Saturn and the Earth are both affected by the solar wind. Belts of energetic particles move around the planets at high velocities – captured by the respective magnetic fields. On Earth the solar wind controls the intensity of the radiation belt – directly and indirectly. On Saturn it differs. The moons of Saturn play a role.
One reason is the size of the radiation belt. Saturn is a big planet and the radiation belt stretches from the innermost ring out to the moon Tethys, 285,000km into space. On Earth our moon is located beyond the magnetosphere and the radiation belts – but on Saturn the moons interact with the radiation belt and modify it. See https://phys.org/print428605174.html