Distilled vs tap
If you are trying to replace evaporated water, distilled is most like the water that has left the tank. As water evaporates, it leaves behind the salts and minerals.
If you replace with distilled, you are not adding any extra salts or minerals to the tank. If you are replacie with tap water you are adding extra minerals.
If you have small losses and large water changes, the slowly increasing concentration of the water is not a big deal, but with high evaporation and small water changes, the effect is magnified.
In most cases, it is not a big deal, but it is a reason to test your GH once in awhile, just so you can see if it is rising very much.