As always, mwestwood writes a fantastic addition to our discussions! I love the quoting of Macbeth, thank you for that!!!
My opinion is that connotations are the key to most semantic meaning and so if you deem a group of bad kids a "gang", it would be inappropriate to deem the same name and meaning to a group that acts completely differently altogether.
A group is a group. A fraternity is a fraternity. A gang is a gang. Period.
If you write, you are a writer. If you report, you are a reporter. The writer and the reporter both write, but they use different techniques, topics, and formats. To call a reporter a "writer" would be to reduce the job of a writer who, by connotation, does far more than repeat information to the masses.
Hence, fraternities and sororities are academic and social organizations whose purpose is to filter student demographics either by ethnicity, by academic interest, or by social interests. A gang is a simple group of naydoers who like to cause mischief. No- a gang and a fraternity or a sorority are not the same thing in whatever contextual definition you wish to analyze it.