Spring is likely to have more metals and minerals in it than distilled. Spring comes out of the ground, where all that's found, so it's not surprising. Distilled water is obtained via evaporation. They take water, evaporate it, catch the vapors and let them condense. Since water leaves behind impurities when it evaporated, the caught vapor is (in theory anyway) pure water. As long as they use no metal tubing or accessories in the distillation process, the water should be good. If it were me, I'd go distilled and stay away from spring water.
*As far as distilled water being deadly to fish, this is only partly true, and only in freshwater. In saltwater, the salt mix you add puts required electrolytes, minerals, and nutrients back into the water. In freshwater, you don't add anything like sea salt, so the fish do not have the necessary minerals in the water, and they die.
125 gallon saltwater: 55gal sump, 4 Blue-Green Chromis, Purple Tang, True Perc, Firefish, Royal Gramma, 5 Ricordea, Bubble Coral, 15 Pulsing Xenia, Green Star Polyps, Deresa clam, Green-Tip Torch Coral (about 11 "heads"!), Orange Montipora Cap, Purple M. Digitata, Green Slimer Acro. Yongei, 3 Orange M. Digitata, Pink&Green Acro. Millepora