Hard water prob

I wanted to start washing my face with distilled water so i went to the pharmacy to get it. The lady said they dont have it and adviced i can find it in any supermarket.also cheaper by the gallon. So i went to the super but the gallons are labelled ‘demineralized’ water. So my question is, is demineralized water indeed safe to use for washing my face as opposed to ‘distilled’ water?