The symptoms of right hemisphere brain damage can actually vary a lot. I meet patients with RHD (right hemisphere damage) frequently at the hospital I work at. Even though some of their symptoms are the same, the intensity of the symptoms vary based on the type of injury they have.
Different parts of the brain are responsible for different functions, so what symptoms appear depends on which exact parts in the right brain are affected. For example, one person with right sided brain injury might not have many physical problems but a lot of cognitive ones. Someone else might be doing better cognitively but with physical coordination and control problems. So it depends on the individual and the type of damage.