There are three types of magic: Arcane, Divine, and Innate.
Wizards, Sorcerors, Warlocks, Summoners. There are many types or practitioners of arcane magic but they all create their spells with the same techniques. By using incantations, gestures, and material components practitioners of arcane magic can manipulate the fabric of reality (called the weave) to create effects.
Druids, Priests, Clerics, Rangers. Many spellcasters produce magical effects by drawing power the gods or nature itself. The druidic language allows those with a connection to nature to call on the spirits of the natural world for aid. Servants of the gods invoke the hidden names of deities and if the god they serve favors them, the servant is granted power.
Many creatures have magical abilities that come not from knowledge of the weave or a higher power but from their own bodies. This raw magic can be a byproduct of other magic or a biological function like a dragon's breath.
Common Perceptions of Magic
Most of the people of the world never cast a spell themselves. Those that have ever seen a spell cast have likely only seen small effects produced a traveling illusionist or adventurer. The greater powers of magic are largely unknown and feared by the common folk. Sometimes people dismissively call spellcasters "mumblers," mocking their incantations. Nobels and the wealthy are more familiar and receptive to spellcasters and often seek their services. The ultimate status symbol is to have a spellcaster in residence and scholars covet these positions for the opportunity to research in comfort and gain social status.