Aspects are what are most fundamentally important to you as a Person AND as a Character. Aspects define your strongest Core Value.
Classes are how you interact with that Core Value as a Person AND as a Character. Classes define your relationship with that Aspect.
Classpects function as a Narrative Device AND a Character Building Device. They have Passive AND Active usefulness in constructing your story and your character. They will directly contribute to the foundation of your character, AND the active progress of the story. A weak understanding of a Classpect leads to weak foundational work.
If you can figure out the Classpect of a character, your work is not done there- but it does provide an insanely valuable set of directions if you understand how the Hard Magic System works. If you understand how Classpects work- and, more importantly, how that specific Classpect you are toying with functions- then writing the rest of the character will most likely come somewhat naturally.