SPOILERS (THESE TERMS ARE EXPLAINED IN CHAPTER TWO)
Sorcery refers to the usage of magic circles, spells, or sacrifices to summon and bind demons for the purpose of using them to perform magical tasks. “Demon” is a generic term; what would normally be called “fairies” and “gods” are simply called “demons”.
Invented by Zero, magic is a new way of obtaining the power to alter reality/perform magical tasks without summoning a demon. As a result, magic is safer, simpler, and more powerful than sorcery. Experienced users are also able to cast spells without enunciating them.
Translated from JP wikipedia by Aer