Do (simple, inorganic) salts ionize completely in water when they dissolve?
When a salt, no matter which salt, or any other polar compound is exposed to enough water, then its polarized molecule parts, depending on its polarity, become attracted to the oxygen or hydrogens of the water, which will result, starting with the outermost molecule layer, in the complete dissolution of the compound. Within this process both the positively and the negatively polarized sections will get surrounded by water molecules (= hydration shell) and thus shielded from one another. In this state the original compound(s) have (theoretically) disappeared completely and the two containers will indeed be identical. Possible back reactions will (mainly) result in the most energy efficient compound for the particular experimental conditions and have the same chance in both containers.

When you now evaporate all the water you may get various compounds and mixtures depending on what was dissolved.  

PS: I'd say "of equal molarity" or "they are equimolar", but my mother tongue isn't English, so there might be a more elegant way.