why do the dry sodium chloride and the solutions of sodium nitrate and sodium chloride show the same color?

Answer 1

In terms of clear crystals and clear solutions, they do not absorb light in the visible range.

In terms of flame test, they all contain sodium ions, which give off a yellowish light when heated.

Answer 2

Sodium Chloride and Sodium Nitrate show the same color in solution, because the color comes from the metalic sodium complex formed. And the sodium ion will always make the same complex in the same solvent.