you have solutions of MgSO4(aq) and MnSO4(aq). what would you add to distinguish between the two?

I would add NaBiO3 to an acidified solution(HNO3 or H2SO4) of the MnSO4 and heat. Mn is oxidized to MnO4^- which is purple.

Or, add NaOH. Mn(II) forms an initially white ppt which oxidized in air to MnO2 (actually hydrated Mn(OH)2). The oxidation step can be hastened by the addition of H2O2.