I think the distinction between modern "gangs" and traditional "mafias" and "mobs" is a false one.

Groups of poverty stricken, young people adopting similar cultural identifiers and supporting themselves through crime has almost certainly been going on since before the beginning of recorded history.

There are records of youth gangs in 17th century London who used colored rags to identify themselves just like blood or sureno would today. Furthermore, urban youth gangs have existed in America since at least the early 19th century, and rural gangsterism is probably older.

Modern gangs have different provenances depending on their specific circumstances, but most of them were initially just groups of teenagers from a specific area who decided to start committing crimes. Some gangs (Latin Kings, Hells Angels etc.) developed from social clubs.

Also as far as your question about whether or not gangs grew out of the mafia, usually it's the opposite. Lucky Luciano, Meyer Lansky and the other guys who created the American mafia as we know it all got their start in disorganized youth gangs in their neighborhoods. More recently BMF (a highly organized African American Drug trafficking organization) generally recruited from veterans of youth street gangs.