Er, I might be able to offer some insight into this - I know very little about vaping, as i've only been off the analogs for 7 days, but I'm a window cleaner, and I use one of those telescopic pole systems you might have seen - bear with me, i'm going somewhere with this -
Basically, we use purified water for cleaning the windows, for various reasons I won't bother to go into here. The water we use is de-ionised. We make that by running a reverse osmosis system - basically tap water goes through 3 sediment filters, then through a reverse osmosis filter, then a de-ionisation tank. What comes out is in theory, pure H20.
Straight from the filter, i'd imagine it's pretty damn pure. We use TDS meters to test the purity, and they measure the total dissolved solids (stuff in the water that isn't just h20) in PPM, or parts per million. Any de-ionised water you buy will likely have a percentage that isn't h20. My setup outputs between 2 - 10 PPM depending on how new the filters are.
Distilled water is water that has been heated to steam, then the steam is condensed and is in theory pure h20.
I'd imagine that if you got pretty good, pure deionised water, it'd be as good as distilled, as it gets heated up when you vape it. The stuff that isn't h20 would I imagine get left on the coils.
The danger with distilled AND deionised water, is that it has nothing in it like the chlorine and other chemicals that are in tap water - chemicals put there (amongst other things) to prevent bacteria and viruses having a little orgy and raising a small colony in your water tank.
The theory goes, that such untreated water, if left, can become fairly toxic. The big danger for us window cleaners is legionnaires disease - since we always have fairly massive tanks of purified water either at home, in our vans, or both. For example when I go out to work I take about 250 litres of deionised water out with me every day.
So whatever you get, use it quick, keep it chilled, I guess.
Remember, i'm a noob to vaping, and not a doctor, just a simple window cleaner, but that's what I know about distilled water, deionised water and the associated dangers.
So there you go. Hope this helped or was at least a little interesting. All the best and happy vaping!
Neilythere.