Question: With the legalization of moonshine in many US states I've been wondering what are the big differences between Moonshine and Vodka?

Both are clear spirits made from whatever grains/starches are available. Both can be fairly high proof.

Is it all just an Appalachian that is tied to their origin?

Answer: 
> 
> Moonshine is any alcohol that is made illegally. It is usually make in
>  small batches
> 
> 
> 

In most cases if you are able to buy 'Moonshine' from a store it is generally not real moonshine 

I believe that it's called moonshine because it was illegal to make, so it was usually distributed at night time under the moonlight hence the name 'Moonshine'. It was popular to make as they could produce a high % drink very quickly but in most places there is a legal amount of time you have to distill an alcohol for. Moonshiners did not adhere to these rules hence why the drink was illegal. 

In places where moonshine has been legalized I would not consider it moonshine anymore as that just means they have allowed the distillers to bottle after any time they want in the processes instead of giving a set time for minimum distillation .

There are some legal Moonshine distilleries that label their alcohol as moonshine but most of these are playing on the growing trend of moonshine as all of these are still legit distilleries. They pay all the taxes and ship out there product so this is perfectly legal and they call it moonshine. While this is not a original moonshine, as it is all legal. Moonshine can be any really high proof alcohol but once that alcohol is sold and distributed legally it just becomes the same as any-other spirit and loses the true nature of being moonshine. 

[source](http://www.distillingliquor.com/2015/01/21/types-of-alcohol/)
If you want to be a traditionalist, it's not really Moonshine unless it was produced illegally, without all the proper taxes and such. Anything you buy in the store could more accurately be called white liquor, grain liquor or corn liquor, depending on the mash stock.

A key feature of both legally and illegally produced Moonshine is that it's unaged. It goes straight from the still into the jar or jug. This facet was born of the need to make quick profits, the need to minimize the amount of evidence on hand in the event of a raid, and by extension, get your liquor into the hands of paying customers before the revenuers could find it.

Physically speaking, there is no real difference between vodka and moonshine. Both are unaged neutral spirits, usually cut with water to increase volume and produce a more drinkable product. The difference is mostly geographic. Moonshine, at least commercial varieties, can easily be called American Vodka, much like Poitin could be called Irish vodka.