Dialect is a regional variety of language, with likely differences in vocabulary, grammar and pronunciation. In fact, a dialect is often a whole language rich with literature and grammar et al.
A dialect can also be one of a family of related languages. French and Italian are called Romance dialects and English Germanic.

Vernacular means:

An ordinary language or the everyday language of the people in a country or a region, as distinct from official or formal language. Vernacular is just a spoken language in the sense that it is the common spoken language of a people, as distinct from formal written or literary language.
Vernacular in Biological terms could mean just a Common name like a common name of a plant, animal or other organism, as distinct from its scientific name.
In Architecture, vernacular means a building designed in an ordinary building style using the local architecture of a place or people, especially the architectural style that is used for ordinary houses ...more

Dialect is the form of a language which is peculiar to a specific region or social group. While vernacular any regional language other than commonily used language like English

The vernacular is the language spoken by the ordinary man [ie, non-academic]

Dialect is the form of a language which is peculiar to a specific region or social group.

There is a subtle difference, in that [for instance] the poet Robert Burns wrote his poems in the Scots vernacular, whereas D.H Lawrence wrote poems in Lancashire dialect

The usage or vocabulary that is characteristic of a specific group of people in the use of a language other than mother tongue is dialect. Immigrants to England speak a dialect of English, appearing bit odd.
Vernakular is the everyday speech of the people (as distinguished from literary language).