Distilled water is the steam from boiling water that has been cooled and returned to its liquid state. It is a popular belief that distilled water is the purest form of water to drink.
All water, no matter where it comes from, whether a natural spring, artesian well, or regular tap is likely to have trace but safe amounts of minerals, bacteria, pesticides, and other contaminants.
Distilling helps to remove all forms of impurities. In the processm it also removes more than 99.9% of the minerals dissolved in water. 
Filtered water, however, is tap water that has been run through filters to remove chlorine content (this improves the taste) and other things such as bacteria  and some chemicals. There are different types of filters to remove different properties. Most bottled water is filtered in some way.
Is it safe to drink distilled water?
Distilled water is safe to drink. As opposed to tap and bottled waters, it has a flatter and blander flavor, therefore you might not enjoy the taste.
By heating water to a high temperature and collecting the steam, companies may create distilled water. Impurities and minerals are taken out of the water by this method.
Drinking distilled water, according to some sources, is said to boost health and aids in body detoxification. Others assert that drinking distilled water might damage your health because it leaches minerals from your body. These statements aren’t totally accurate in reality.