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 derives (supposedly) its name from transporting it at night to avoid detection.

Moonshine was made a lot in the mountains because of the inaccessibility of where the mountain-folk would hide the Stills and the abundance of fresh mountain springs. They could also make the moonshine high proof to maximize cost/drunk ratio (I know it sounds close minded but not a ton of reasons to buy high proof alcohol). 

Liquor is measured in proof which is just 2x the alcohol % listed - 40% Vodka is 80Proof. There is not commercial grade 200 proof moonshine mainly because of physics. 

> 
> This is because ethanol is not an ordinary mixture, it’s an azeotrope. Instead of boiling purely and separately at two different temperatures, its vapor will form a certain proportion. Steam from alcohol is 95.57 percent alcohol. Get a pot of 95.57 percent ethanol boiling and the steam will be 95.57 percent ethanol right down until the last drop evaporates.
>  [Source](http://io9.gizmodo.com/why-cant-you-make-liquor-thats-100-percent-pure-alcohol-1701953611)
> 
> 
> 

There are probably other moonshiners across the country; but, the origin is steeped in the Appalachian Mountains. Junior Johnson (a NASCAR Driver) started his own line of spirits and has "moonshine." They aren't over 100 proof though...
As a detail and hopefully and appropriately informative aside for this topic:

In chemistry lab there are two alcohol solvents used:
1. Medical Grade (surgical alcohol) = 95% Alcohol (getting that last 0.57% is very time consuming to achieve)
2. (benzene) Alcohol = 98% Alcohol (with 2% benzene still in solution with the alcohol)

[Benzene is used to drive off or get all of the 5% of water out of distilled alcohol](https://www.google.com/search?q=Benzene%20is%20used%20to%20drive%20off%20or%20get%20all%20of%20the%205%25%20of%20water%20out%20of%20distilled%20alcohol&oq=Benzene%20is%20used%20to%20drive%20off%20or%20get%20all%20of%20the%205%25%20of%20water%20out%20of%20distilled%20alcohol). The (benzene) Alcohol will make you sick because of the benzene. 

Surgical alcohol provides the most wonderful drunk. It is a body drunk with zero dizziness. 

Dizziness comes from the long chain fusel oil(s) (alcohols) in fermented alcohol. Fusel oil alcohols are not present in surgical alcohol. All fusel oil alcohols boil off at a different, slightly higher temperature than ethanol (drinking alcohol). Sloppy or rushed distilling gets the higher temperature fusel oil alcohols coming over with the ethanol. Really sloppy and very rushed distilling gets the first run methyl alcohol, methanol . . . which causes permanent eyesight loss. Long chain alcohols cause much of the hangover effect of headaches.

Yeasts produce fusel oils when they struggle to produce higher percentage alcohol levels in wines and beers.
[https://www.google.com/search?q=FUSEL+OIL+ALCOHOLS](https://www.google.com/search?q=FUSEL%20OIL%20ALCOHOLS)