Evaporation is changing something from a liquid to a gas. Liquid water into water vapor is still water (H2O)

Distillation is removing impurities by heating and cooling. Think of distilling tap water and having salt buildup left behind. Or distilling whiskey to get rid of impurities. It's still whiskey/water at the end, just less junk in it.

Sublimation is going from a solid to a gas, like dry ice (CO2) into regular CO2 gas. All the same stuff, just in a different state.

What you were talking about would be more like electrolysis of water. With stainless steel, tap water and a battery, you can put two pieces of stainless steel (or gold, silver, or platinum, but stainless is easier to find. I used hose clamps when I did this) in water and connect a battery across them. The energy of the batter actually splits the water molecule (H2O) into hydrogen (2H) and oxygen (O) which is actually splitting the molecule into its atoms.

You can tell it split and not just water vapor because you can put a lighter to the bubbles coming from the - side and they should make a small "pop" noise, which is the hydrogen burning with the oxygen into the air and making water vapor. If you collect a bunch of the bubbles from the + side, you can re-light a blown out match/candle that's still hot because it's pure oxygen.

It's weird that water can be broken down into two very volatile fire parts when water is used to put out fire, but that's chemistry for you.

So yeah, long story short, splitting (some) molecules is fairly easy to do and makes some drastically different properties than the original thing!