Not all symptoms of a disease are caused by your immune system’s reaction. Viruses and bacteria often cause different symptoms because they host themselves in different cells or tissues of your body.
Also, yes your body reacts differently to different diseases too. We categorize our defence mechanisms into two categories: innate(or nonspecific) which always acts the same way, and adaptive(or specific) which changes the specific disease. Explaining how they differentiate between different pathogens is a bit much for a Reddit comment, so I [link](https://www.ncbi.nlm.nih.gov/books/NBK279396/) this NCBI article which explains it pretty well and with easy enough-to-understand language.
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