A wizard is taught magic; reading books and training magic like a technical skill that uses their understanding of the theory around it. 

A sorcerer is someone born with magic; somewhere in their bloodline a magical creature or person was involved. They control magic instinctively and are less learning more magic but the length of their natural capabilities. 

From a gameplay point of view Wizards are intelligent and specialize in a type of magic.

Sorcerers are charismatic and can bend some rules based on their background; like getting to use some healing spells if your bloodline is touched by the celestial, or dealing extra lightning damage if it's a storm elemental. Things like that.