Those are one and the same. Vulgar Latin refers to the dialect spoken by the people in any given part of the empire, there was not one Vulgar Latin. There were many, the latin spoken in Italica in Iberia would have been different than that spoken in Londinium.

In short, because Vulgar Latin is the language people actually spoke.

"Classical" Latin was the language spoken around the fall of the Republic. By the fall of the Empire, spoken Latin was very, very different. Imagine trying to understand spoken English from perhaps a thousand years ago and you have some idea. When the Empire fell, the various provinces went into a period of isolation where the various "vulgar" Latin dialects mutated into the Romance languages.

That we still speak Classical Latin at all is due to a quirk of Roman society: they didn't like writing in the Vulgate. I don't really know why. Class snobbishness? Because they all read from the same, limited, pool of literature? Maybe someone could clarify.

Anyway, while spoken Latin kept changing, written Latin remained more or less static. It would be like Americans speaking modern English but writing like Chaucer. While the spoken language went right on mutating, Classical Latin remained static in books. A very few could also speak Classical Latin, but they had to be trained to do so, as it was, by then, a specialized skill.