Question details: For example, for a GI bug, some of my kids will have vomiting, others will have diarrhea, or one unfortunate one will end up with both.

Differences in either genetics and/or exposure (dose) might lead siblings to have different symptoms to the same illness and the two reasons aren’t mutually exclusive.

No two individuals have the exact same biomedical profile, not even identical (monozygotic) twins*.

These differences form the essential basis for differences in symptoms and severity for the same illness among individuals. However, apart from genetic and immunity differences between hosts, differences in severity of exposure could also explain why this happens, with the sibling with greatest exposure, i.e., dose, more likely to suffer the most severe symptoms. The same sibling repeatedly suffering more severe outcomes for shared illnesses would suggest greater likelihood of underlying genetic difference(s) being at play.

To successfully infect means to first successfully enter a cell, replicate inside it and finally spread to neighboring cells and beyond. Each disease-causing microbe thus evolves to express molecules that mimic those that bind certain cell-surface receptors and this process then serves as its entryway into a particular cell. This preference of a particular microbe to infect certain tissues is its Tissue tropism – Wikipedia. For e.g., the cold virus, Rhinovirus – Wikipedia, and Influenza – Wikipedia primarily target the epithelial cells of the upper respiratory tract, Viral hepatitis – Wikipedia the liver, etc.

Though cells obviously differ in the panoply of what they express on their surface, there’s also considerable overlap between different tissues and these overlaps differ between individuals, both in strength and variety. Thus, given the processes of genetic and somatic recombination, and epigenetics, even related individuals differ in their relative susceptibility to various disease-causing microbes.

This is why some people might get Zika fever – Wikipedia and never know since their symptoms stayed so mild while others may get fever (systemic involvement), joint pain (musculoskeletal) and rashes on their torso (skin) while still others could develop debilitating muscle weakness and pain, Guillain–Barré syndrome – Wikipedia, symptoms that could even be life-threatening.

With a GI tract illness, only vomiting suggests a stringently self-limiting infection that stayed restricted to the upper GI tract, diarrhea suggests a spread into the lower GI tract while both vomiting and diarrhea suggest the most severe outcome, i.e., persistent infection effects in both upper and lower GI tract. Again, simple dose differences in initial exposure could be a trivial explanation for a one-off outcome difference of this kind.

* Tim D. Spector’s long-term studies on identical and fraternal twins show that ‘twins rarely die of the same disease‘ (Why do identical twins end up having such different lives?).