... which kind of points to the indicator that "Alzheimer != Alzheimer", implying that too many diseases with the same side effects are categorized together?

A lot of virological and parasitical components have historically been wrongly associated with genetic markers, too. Toxoplasmosis parasite comes to mind.

[1] https://en.wikipedia.org/wiki/Toxoplasmosis

[2] https://en.wikipedia.org/wiki/Toxoplasma_gondii