Not sure if the buttons appear to be so similar for you due to your screen settings or potentially color blindness? If the latter the iNat staff might look into making that clearer.
But no, a hard disagreement refers to the evidence specifically, which could mean 1) that the evidence disproves it is that species, or 2) that there just isn’t enough evidence to prove it is the species. This has been discussed at length in many other forum topics for example this one https://forum.inaturalist.org/t/change-wording-used-by-the-system-when-downgrading-an-observation-to-an-higher-level-taxa/3862/
The strings you mentioned have to be considered as paired with the text at the top of the pop up.