Refraction and non-refraction shader water look extremely different
The refraction toggle in the water shader options is not just a refraction toggle. It changes a lot of different techniques that the water shader uses around, and also their mixing/blending values, for reasons that have nothing to do with refraction itself. For example, refraction water is significantly less reflective than non-refractive water, even in areas of the visible water surface where the refracted underwater areas are invisible and have no influence on what the player can see.
If both versions are desirable, each difference should be individually configurable. Otherwise, the two versions of shaded water should be brought in line and unified. The only differences should be 1) whether the underwater surface has actual refraction effects applied 2) applying fog below the water surface in refraction mode (since doing so for non-refraction water would be kind of difficult).
This issue is distinct from the various general refraction and non-refraction water bugs: it only concerns the fact that they are in general so different, not the individual differences.