Short Answer 
A mage is an individual knowledgeable in magic, emphasizing wisdom and intellectual mastery. A sorcerer has innate abilities to summon supernatural forces but is often viewed negatively due to their selfish motivations. A wizard, on the other hand, is formally trained in magic, using wands and structured spells, combining scholarly knowledge with practical application.
Step 1: Understanding the Mage
A mage is typically characterized as an individual who is highly knowledgeable in magic. They often possess a sense of wisdom and scholarly understanding of magical practices. This term is broadly applied across various cultures and can indicate a deep connection with the arcane arts, emphasizing skill and intellectual mastery in the field of magic.
Step 2: Defining the Sorcerer
A sorcerer is usually depicted as someone with a natural talent for summoning and controlling supernatural forces. They are often viewed through a more negative lens, as historically, sorcerers were associated with selfish motives and the pursuit of personal power. This innate ability often places them in a distinct category, differentiating them from those who learn magic through study.
Step 3: The Role of the Wizard
A wizard, much like the characters in the Harry Potter series, represents a practitioner of magic who has undergone formal training. Wizards utilize wands and have a structured understanding of spells and magical rituals. Their portrayal often combines scholarly characteristics and the ability to implement complex magical constructs, making them a unique figure in the realm of magic.