What's the deal with vodka?

From what I understand, it’s supposed to be made of potatoes. But I have here before me a bottle distilled from rye. Is this an acceptable variant, ie the process by which it is made is more important than the details of the ingredients? Is it just a “ripoff” of sorts and is really just some other kind of liquor? If vodka can be made from potatoes, then why don’t they do that?

Vodka was traditionally made with potatoes in Poland and Russia (the word vodka come from the Russian word for “water”), but you can distill it from whatever you’ve got lying around, or whatever’s cheapest – which usually means some sort of cereal grain.

Vodka is made from a mash of pale grain or vegetable matter
http://www.tastings.com/spirits/vodka.html

While vodka can be made from potatoes, it’s usually made from grain, because it tastes better that way.

Vodka only requires two ingrediants: alcohol (ethanol) and water. You can get ethanol from many, many sources. It really doesn’t matter which one it comes from because it is the same compound in any case. Mix the ethanol with whatever volume of water you want to get the desire proof and viola, instant vodka.