I believe the primary difference is the shelf life / preservability. May also be related to the amount one buys and the intended use, as there are many besides nebulizing. Peroxide degrades and becomes less active when exposed to oxygen. I personally used the 3% topical solution commonly available at pharmacies. The topical solution does not say "food grade" but it does say "for use as a gargle or rinse" right on the label, below "for treatment of minor cuts and abrasions." So I didn't worry. Also, at the time I first started, I was desperate. I have seen variations on the dilution recipe, from 2.5cc - 6cc of peroxide to 300cc of saline. I instead mix it fresh each use, 0.04cc to 3cc. The large quantities are recommended in order to measure easily, but I instead used a diabetic syringe that is designed to measure in units of 0.01cc.

I have no clue on the difference between an atomizer and a nebulizer, other than possibly the intended purpose. But a spray bottle would present difficulties as far as getting it into the lungs, which is how the nebulizer is used, so I'm not sure if it's a viable alternative.