Distilled, de-ionised refer to the method used for purification, not the water itself.
Distilled water is water that has been boiled to a vapour and then allowed to condense again. The dissolved impurities are all left behid in the boiling pot (this is what limescale is). Distilled water is very pure, however, distilling water is a relatively expensive and slow process.
Rainwater is essentially "distilled" by evaporating from the sea, lakes and rivers and then condensing again as rain. Thats why rain water is very pure, and if you could collect enough of it, would be perfectly okay for window cleaning.
De-ionised water, is water that has had the "ions" removed. So what's an "ion"? Ions are the dissolved solids. For example, Salt is a compund called Soduim Chloride, literally a combination of Sodium and Chlorine.
When you dissolve salt in water, these two elements seperate into charged particles called "ions" The sodium has a + charge, the chlorine a -
Special resins remove the ions from the water, hence the term "de-ionised" water.
(Technically, they don't actually 'remove' the ions, but they exchange them for H+ and OH- ions. These, being oppositely charged are attracted and then combine to form H2O. Or water, of course!)
-Philip