The meaning is the same, "sostantivo" is grammatical jargon ;) But be careful: a person name can't be a "sostantivo" but only a name ;)

"Qual è la differenza fra le parole sostantivo e nome in Italiano?" There is no difference between them. Grammatically have the same meaning. To be more specific, "nome" is referred only to person'name, instead "sostantivo" referred to people, things and animals.

Nouns (Sostantivo) are those words which can occur with articles and attributive adjectives and can function as the head of a noun phrase. A name (Nome) is a word or term used for identification.