(These rules have been altered you can still access the original here)
Sway is how we measure things in T13. If you want to clobber a exoskeleton-clad villain through a building, you need Sway to measure how hard you hit.
Sway translates directly into Difficulty, rolled dice Scores and other such nonsense. It is the balance about which the game pivots. Sway is the lifeblood of T13, it drives the narrative, defines the Characters and acts as a measure of Wealth, Experience and Power.
Chi is a more refined, divine form of Sway. It cannot be manipulated by Grunts or Goblins, but can by Demons and Mercari (and most Paradox Warriors, Eelafin and Bulmäs). You can find out more here.
Yarn is the most refined form of Sway. It cannot be manipulated by anyone but Demonlords, Grand Mercari or Solos. You can find out more about what Yarn can do here.
Twists are the dark reflection of Sway. Only Goblins, Demons, Demonlords and their ilk can manipulate Twists. You can find out how here.