According to Webster online these are very similar terms. But in looking at the definitions I think that a vernacular can be whole separate language while a dialect is just a modification of a language. Perhaps you will get a better answer from someone else. ;-)
vernacular "1 a: using a language or dialect native to a region or country rather than a literary, cultured, or foreign language b: of, relating to, or being a nonstandard language or dialect of a place, region, or country c: of, relating to, or being the normal spoken form of a language"
dialect "1 a: a regional variety of language distinguished by features of vocabulary, grammar, and pronunciation from other regional varieties and constituting together with them a single language <the Doric dialect of ancient Greek> b: one of two or more cognate languages <French and Italian are Romance dialects> c: a variety of a language used by the members of a group <such dialects as politics and advertising — Philip Howard> d: a variety of language whose identity is fixed by a factor other than geography (as social class) <spoke a rough peasant dialect>"