Set Apart started as an Exalted hack, or maybe more clearly, as a proof-of-concept for Exalted as a post-apocalyptic setting, something that had gotten sorely lost in recent years. With the inclusion of the tarot elements, it's turned into something much more.
Each of the Exalted splats (Solars, Lunars, Sidereals, Abyssals, and Dragon-Blooded) get split into two Set Apart splats that explore different aspects of that Exalted's themes and purposes. Additionally, there is a set of five infernal splats that characters can become, based on their previous type.
There are no alchemical splats, because alchemicals are dumb. For example (of the types, not of alchemical stupidity)!
The Emperor and The Chariot are Solar splats.
The Emperor deals with leadership, rulership (two different things there), and glory. The Emperor is predominantly Hard, and secondarily Cool.
The Chariot deals with perfection and competition, being the best. The Chariot is predominantly Cool, and secondarily Hard.
When a Chariot or Emperor falls to infernalism, they become The Tower. The Tower is all about rampant destruction.