I imagine Discord and Chyisalis to be a part of a vicious street gang (think the Purple Dragons from "Teenage Mutant Ninja Turtles") called "The Changelings", and Luna was once part of that gang, where she earned the nickname "Nightmare Moon". Then Luna abadoned that name and that gang and became the principal of Canterlot High.
Cadence is the mayor of Canterlot.
You're right, I forgot that Cadence foalsat Twilight. My idea for Nightmare Moon is that Luna got jealous and so went crazy for a bit before being sent to jail. She then came back after realizing that she was acting like a child