I think the exact function differs depending on which source material is used, but generally speaking, Wizards have to read their spellbooks and store the written incantations in their mind for later use, and have to repeat this every day to keep the spells fresh in their minds. They have no natural inborn magical capability on their own and have to study for years in an academic setting to learn their craft. 

A Sorcerer, on the other hand, does have some inborn magical capability, usually from a magical creature in their bloodline, like DeadPixel said. They do not have to memorize spells in the same way a Wizard does, instead drawing their power from within themselves. 

It's sort of like the difference between having a mod installed in a video game or having to type out cheat codes to achieve the same effect. The player with the mod will have their stuff work automatically while the player with the cheat console will need to type out codes for each thing.