These small differences between tap water and distilled water should not produce any noticable difference in ice cubes, however.
A less subtle difference might arise from the fact that many taps "aerate" the water by passing it through a fine mesh with an air intake. Tap water out of most taps has quite a bit of air dissolved in it. If you leave a glass of tap water out for a while you may notice tiny air bubbles forming on the side. If you freeze the water quickly, the ice will form before the air has a chance to bubble out. The bubbles will form anyway inside of the ice cubes because the dissolved air does not fit into the ice crystal lattice. So if you look at ice cubes made from tap water compared with distilled water, you might find that the tap water ones are not as clear and transparent as the distilled water ones because of all the air bubbles inside. But this isn't a fixed property of tap water or distilled water, just in their handling (you can dissolve air in the distilled water too!).
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