It isn't a strict subset. Vaccine risk includes cellular expression of spike protein in a scattershot way throughout your circulatory system (mRNA vaccine). Viral infection expresses whole virus, not just sprotein, and isn't targeted at or tramitted through the circulatory system, but instead the respiratory system.
There are differences, and s-protein expression may trigger mild autoimmune disorders.
>Then the virus variant itself would cause autoimmune disease
You clearly have no idea what you are talking about or why the GP comment mentioned an autoimmune disease specifically. mRNA vaccines express specific proteins whereas the virus expresses entire viral molecules. A novel protein expression could cause an autoimmune disease because the novel proteins couls cause the immune system to attack the cells producing the isolated proteins, a problem you wouldnt have with cells producing entire viral bodies.
There are differences, and s-protein expression may trigger mild autoimmune disorders.