What is the difference between nouns: wilderness and wild. If we refer to the film "Wild" with Reese Whitersoon, we might name it movie about self discovery in the wild or in the wilderness?

Wild is mostly used as an adjective. There are a couple of expressions where it is a noun.

 "On this tour you can see native species in the wild." 

"in the wild" is an expression meaning in their unaltered natural environment.

Another expression is "in the wilds of Borneo" - The plural form is used in the particular expression to mean all the wilderness areas in a country, state, or other region..

WIlderness is always a noun. It means a specific area or region (usually covered in dense vegetation ) that has not been altered by human activities. It is a place where people do not live and cannot live. One can easily get lost in the wilderness.