I already know that the Latin spoken by most of the population of the Roman Empire and the Latin used in more formal circles were different(The former being Vulgar Latin and the latter being Classic Latin).
However I am interested in knowing how different they were, were they considered entirely different languages?, or was the situation equivalent to what happens with Standard English and the different dialects(Ebonics, Irish, Australian, British, etc) of it?
I've written here and here about Classical Latin's relationship to its vulgar cousin. The short version is that there is no single "Vulgar Latin." Vulgar Latin is simply the colloquial form of the language, as opposed to the literary form, and since everybody speaks with different personal idioms it's hard to reduce it to clear grammatical rules. Some things, such as the simplification of case structure, elipsis of common verbs, and a few rather bizarre idioms are pretty obvious to us--but while what Cicero writes in many of his letters might be indicative of a form of Vulgar Latin it is certainly not the same sort of Latin that some shmuck in the Subura would be speaking, which itself would not be the same sort of Latin that a provincial would speak