Minerals and other impurities have been removed from distilled water, the same can be said for water which has been treated with reverse osmosis. Sterile water is water in which microorganisms have been killed. Sterile water may or may not have minerals and other impurities removed and distilled water may not be sterile.
The concern is with mineral deposits. Most water which has undergone a process to eliminate or decrease the mineral content has most of the bacteria, etc. removed as well. Water is boiled in the ditillation process which kills most everything.
It is better to use purified water in your humidifier, but using tap water isn't a big deal. I use it when I travel or am too tired to get water back in the kitchen from my Purr filter. Tap water is pretty sterile because of chlorination and other treatment processes. If you use it, you will get mineral deposits which are easily dissolved by swishing and soaking your humidifier with vinager.
Bottled Spring Water contains lots of minerals.
Being defeated is often a temporary condition. Giving up is what makes it permanent.
Marilyn Vos Savant
That which does not kill you makes you stronger-Friedrich Nietzsche
Friedrich must of had apnea.