More than you probably want to know:
This is correct and let me try to explain further. "Distilled" has become a term used for water with only very small amounts of contaminants. Distilled water is water that is created through the process of distillation. Basically, in the process of distillation, the pure H2O is boiled out of its contaminants. Deionization by ion exchange accomplishes the same thing and so does reverse osmosis. For most practical purposes any one of these methods is acceptable.
Distilled water required a lot of energy to accomplish and that is why it is not used very much anymore, at least for water. I've run some good sized evaporators early in my career. Besides using a lot of energy the process involved many moving parts and in total a great amount of maintenance. Reverse osmosis not as much energy and maintenance and ion exchange probably the least. This is why the water you buy for batteries and such is made by the latter process.
I've been involved with all three in different applications all of my life. Water is really a very fascinating and unique subject that most people never give a second thought to. Water is everywhere yet water simply doesn’t behave like other liquids. Beside politics this is one of my favorite subjects.