They are exactly the same. I make components for black powder (potassium nitrate) in a nitre bed using organic material. I could take that same material and fertilize with it. An ion is an ion.
They aren't real salts, these "synthetic" fertilizers. The only thing "synthetic" about them are the chelating agents, as mentioned before. Otherwise, they are just bonded ions, same as organic.
Don't get me wrong, I see where you and others are coming from exactly. I use all raw organic materials, but not because of "salts".
Organic releases much slower as it has to be broken down. Less immediate nutrition, more over the long run. I'm learning this the hard way on the hydro bucket lol.
Organic amendments are really only meant for soil structure. "Synthetic" fertilizers are immediate nutrition that can be used in any medium via chelation, but they don't hold like organic. Beyond that, there is no difference between the ions.