The standard way of referring to magical men and women, as opposed to muggles, in the world of Harry Potter, these words were widely used in English long before J.K. Rowling started writing. They appear in books like The Lord of the Rings, The Chronicles of Narnia, and The Wizard of Oz, and have been standard fare in films and television for decades.
The word wizard is from Middle English, a combination of wise and –ard, in the sense of a philosopher or sage. In the middle of the 16th century the word became a term for someone practicing witchcraft, when there was little difference between magic and wisdom. In the early 17th century it evolved to refer to anyone with impressive knowledge or wisdom in some area. We now talk about computer programming wizards, a math whiz (derived from wizard), and wizardly acts.
Wizards have been running around fantasy fiction for generations. From Ursula Le Guin’s famed novel The Wizard of Earthsea to Gandalf and his brethren in The Lord of the Rings, sagely men with beards, hats, and staffs or wands are well known, loved or feared or both, and a part of the modern canon. They all ultimately seem to stem from Merlin, the wizard/sorcerer of the Arthurian tales, though Merlin appears and behaves differently depending on which version of the tales you read or see.
Witch comes from Old English wicca (for a man) or wicce (for a woman), both meaning magic user. This makes the modern use of Wicca a bit peculiar, given that women apply it to themselves to refer to witches and witchcraft. The meaning of witch has varied over the centuries, from a nadir of evil during the Salem Witch trials to the modern colloquial use to refer to an ugly, unpleasant old woman or a wonderfully attractive woman.
Witches too have been appearing in fiction for generations, though usually evil, as in The Lion, the Witch, and the Wardrobe by C. S. Lewis or the Wicked Witch of the West in The Wizard of Oz, Some, however, have been noble and good. In general though witches have not enjoyed the prestige or good will that wizards did. They instead were targets of witch hunts, often drowned, burned, or otherwise tortured into submission, recanting their alleged association with the Devil, and giving up evil.
Wizards and Witches in Harry Potter's World
In Rowling’s stories, wizards and witches are simply two ways of referring to the same thing: a person with magical power. Wizard applies to men, witch applies to women, a distinction quite common in English. This gender-specific usage makes the full name Hogwarts School of Witchcraft and Wizardry a bit redundant or confusing, since there is no clear distinction between witchcraft and wizardry apparent in Harry Potter’s world, and boys and girls are able to attend all the same classes, except where natural talent or interests determine otherwise.
Rowling adds a particular twist to the two words witch and wizard insofar as they apply to any magical person of any age. A body, a girl, even a newborn can be and is referred to as a witch or a wizard. Dumbledore refers to Harry, Ron, and Hermione as “three young wizards” when talking to them in the infirmary at the end of Harry Potter and the Prisoner of Azkaban, so wizard is at times used collectively when talking to boys and girls. Other writers, and fantasy games such as Dungeons & Dragons, have tended to reserve wizard for an older, accomplisher magic user, and sometimes have given the same treatment to witch.
Rowling was hardly the first author of modern fantasy fiction to use witch and wizard as she does. Terry Pratchett established this usage in his Discworld series in the late 1980s, reserving wizard for men and boys, and witch for women and girls. Wizards and witches in Discworld could be good or evil, and often were a combination of both. Discworld even has a school for wizards, Unseen University, in the capital city of Ankh-Morpork, though it is by it is only open to men (with one notable exception), and potential witches are trained separately by older, established witches under an apprentice system.
Rowling also ignores many other common words used alongside witch or wizard, including warlock, sorcerer, and necromancer. Lord Voldemort is referred to as a dark wizard or evil wizard, but a wizard nonetheless. And despite names such as the Death Eaters for Voldemort’s followers or the Order of the Phoenix and Dumbledore’s Army for those that fight against evil, they all remain witches and wizards.