I will see various definitions in acid-base theory that either utilize hydronium, H3O+, or protons, H+, for various definitions. That is, both pH = -log([H+]) and pH = H3O++]). And we will see equivalent definitions for acid dissociation constants and the like.
What is there fundamental difference here? To me it seems that the hydronium definition assumes that the acid is dissolved in water wheres the proton definition doesn't assume that. Is this correct? Then what is "most correct"?