ImSoNotTelling, I think you are right to a degree - the casuals, soul boys, whatever we called them, were the largely working class boys who were into black dance music, clubs, and expensive designer leisure wear, or sportwear as a fashion statement. Most kids who call themselves 'Chavs' today would identify with that, and they would be the closest comparison.
But the phrase 'casual' or 'soul boy' only really alluded to their tastes in clothes and music, whereas 'Chav' started off being more an observation/insult, meaning a feckless, poorly educated young person from a certain social demographic, who displayed dubious anti-social qualities. I think once the phrase came into common usage it was adopted by the WC kids themselves who, whether they fitted the demographic or not, were largely working class, and wore those clothes. They just latched onto the association with sportwear and chunky gold, bling and Burberry, and applied the term to themselves. Like the N word for black people, and the Q word for gay people. Who know whether 'Chavs' saw the irony?
I think if someone refers to themselves as a Chav, it's about tribal identity and what they wear. If someone else from a totally different demographic refers to someone as a Chav it's usually a comment/judgment on their lifestyle and class, or lack of it!