Is there a single word for witches and wizards both, regardless of gender?
Edit 1: Is there a single word for the category of people who do magic (like witches, wizards, warlocks, sorcerers, etc.)?
Edit 2: The usage example comes from a story I made up for my niece. She wanted to know why I was designating male cats who do magic as witches alongside the female cats. Shouldn't they be called wizards, she asked. I then wondered whether there's one word that encompasses everyone who does magic.
I would suggest using either Mage or Magus (plural: Mages and Magi respectively). Both of them convey a gender-neutral magic-user, without giving off a sense of being a mere illusionist.
However, the term "mage" has fallen out of use, with wizard and witch being the standard terms for any magic user. The term "mage" is gender neutral.
I'd consider Mage the more neutral option of the two, as Magus has a slight hint of masculinity from Latin.
Your edit includes what would have been my first choice (sorcerer) (but then again sorceress does exist, as mentioned elsewhere).
With all that in mind, I'll suggest conjurer/or:
"a person who conjures spirits or practices magic; magician"
(Dictionary reference)
The best word for what you're looking for in my opinion is mage, because it has the same root word as magic, it's gender neutral, and it just means magic-user and nothing else. But you're not going to get much mileage out of the word mage outside of a fantasy context.
I would recommend "practitioner". If you want to be specific, you can use the two-word "magical practitioner".
someone who regularly does a particular activity
Even without "magical", it has a usage within certain literary circles. In the popular novel series The Dresden Files, persons who use magic, regardless of the type, are referred to as "practitioners":
Practitioner is a generic term for an individual who can use magic. The word signifies only the presence of magical talent; it has no connotations regarding the individual's power or skill. There are a number of other terms, however, which do have such connotations.
Obviously, this is used within a specific literary world in this case, but the terminology appears even in other articles:
A magician is a practitioner of magic who attains objectives or acquires knowledge using supernatural means.
The Smart Witch: Introduction to Magic:
One thing magical practitioners have in common throughout history and around the world today is curiosity – the quest for knowledge. We are the original inquiring minds who want to know. There is a reason that so many of the first books printed were grimoires – books of magic – on the whole, magical practitioners are great readers.
The major issue as I see it is that the terminology varies depending on the world you're in.
In Harry Potter, for example, witch is the feminine version of wizard... the type of magic they do is pretty much identical.
In other worlds, everyone who practices "wizardry", regardless of gender is a "wizard" and the practice of witchcraft is very different, and everyone who practices it is called a "witch", again, regardless of gender, though most seem to be female. Similarly, a "magician" could be something different entirely.
I believe that "practitioner" or "magical practitioner" is a word that holds none of the connotations of the individual words have.
"Witch" is not necessarily the cognate of "wizard" in any way. A wizard is someone who has developed some form of wisdom (wiz-dom). It comes from Olde English, as the root is "wis", meaning wise. The conversion of that into a personal noun by adding suffix -ard came later as noted below. Its use even then reflected at first and primarily the quality of wisdom as attributed to a person. It has come to mean someone, particularly a male, who has developed magical powers.When and how this happened I don't know.
A witch, on the other hand, originates in Olde English as well, and had both male and female forms, and implied a person who had magical power and this was its explicit meaning. It specifically meant someone with the power to bewitch others, usually of the opposite sex. The human equivalent of a demon of seduction, basically.
Male witches were called "wicca" and females "wicce", and the verb was "wiccian". If you pronounce the c's correctly, it sounds like a tch. So "witchah" and "witcheh". And if someone is "wiccian" you, they are "witchian" you, or "witchin" you. You are "bewitched".
In fact, witches were thought to be more conversant with spirits, and were thought even to have had congress, even sexual congress, with spirits. But perhaps it was more correct to have thought of them as Celtic shamans and shamanesses, and oracles later to have developed into institutionalized priesthoods, mostly Druidic.
So "witch" is far more magical in origin than "wizard", but wizardry has somehow come to be conflated with a notion of possession of magical power.
Magicians, being of a group called "Magians" and referred to as "Magi", were actually a sect of witch/wizards from the ancient Iranian plateau. The costumery often associated with "wizards" comes from that origin, and is reminiscent of a Scythian Magus, perhaps. They were scholars and mystagogues, and priests, not necessarily in that order.
Perhaps it was they, or rather Greek and later European interpretations of them as iconography for their own purposes which transformed "wizard" into something looking like a Persian Magus (or Mage, Magian, or Magician).
So in the end, for purposes of modern (not necessarily RPG/Fantasy Fiction) uses, we could say that witches represent a kind of innate magic with a propensity to charm or fascinate, wizards represent a profound intellect which is often the confluence of intelligence, intuition, experience, and discipline, whereas someone who managed to combine natural magical power with human mental adroitness would be some sort of psychospiritual renaissance being, a magician of sorts.
John Dee and Isaac Newton represent magicians in this sense, and are the modern representation of true Magi (in English terms). Zoroaster would have been a true Magus in his day, although the destruction of the libraries of Persepolis obscure what that would mean in detail, along with the rest of that tradition. Indeed, for all we know, much work was done there which is the forebear of modern science. Hard to be sure. But that's an aside.
Modern witches, in effect, would be female entertainers, and male entertainers, in any line of work or influences, using charm, often accentuated and augmented by psychotronics and other powerful technology. They're all over the place. Wizards are the deeper scientific and Machiavellian minds, working as either modern viziers, or ministers, giving tyrants advice, or in the former case, giving methods and technology to implement such advice. You have think tanks, councils, foundations, centers, and other "round table groups" just full of wizards and witches, acting as viziers for the ruling elite. Perhaps you have some evil magicians working in those folds as well, such as psychological operations officers high up in the intelligence communities, scientists studying dark technological and scientific frontiers in psychical and paranormal, and extradimensional topics.
You have good witches, good wizards, and good magi as well, but they are sprinkled around sparsely, outside the annals of worldly power, being kind to children and devoting themselves to their crafts, refusing to be corrupted.
