One of the main issues here is most people’s understanding of what cancer actually is. The word does not refer to a single disease, but is an umbrella term used to talk about hundreds of diseases. For this reason, talk of finding a cure “for cancer” is pretty vague and only useful when discussing the diseases in general terms.
Not only that, but different cancers have different pathologies and subsequently different symptoms. Even within cancer “families”, there can be many different variants of the disease, with differing cell lines giving rise to the diseases seen. This means that it is effectively impossible to study or cure “cancer” as a whole, and thus researchers divide and sub-divide them to focus in on individual variants.