A witch (the masculine form is wizard, though the equivalence is not always respected) is classification of sentient beings.
A Witch is, in its broadest sense, a member of a sentient species who possesses magic powers which the majority of the other specimens do not possess. Although most non-magical populations consider this to be enough of a definition, there is actually a further distinction at play: some of those "witches" possess magical powers that they inherited from their ancestry, whereas others must rely on magical objects such as wands to perform magic. The inherently magical witches tend to hold contempt for the latter, and refuse to call them "witches", thinking they do not deserve it, and call for them to be called sorceresses instead.
Though some witches prefer to learn to control their powers on their own, most of them go to wizarding schools or have apprenticeships under more experienced magic users. Most of these schools accept witches and sorceresses alike, but attending some of the most prestigious are the privilege of witches.
Not all witches are evil, but most who style themselves as such are affiliated with a "Witching Government" based on the hidden face of the Moon. The witch government has the ability to expell witches who dishonor their society and take their powers away, which has happened several time to Witch Hazel and Magica De Spell. Another recongized witching authority are the Supreme Witches, who live in a mysterious fiery Underworld. They too encourage witches to be evil, and occasionally grant power upgrades to sorceresses on the condition that they use them for evil.
Wizards and Sorcerers
Male magic users exist just as well as female, but they are less well-known. It is impossible to say whether a similar distinction between "wizard" and "sorcerer" exists as between "witch" and "sorceress", as, for instance, Yen Sid, who seems to fit the type of a wizard due to possessing inherent powers, is referred to as a Sorcerer.