The famous self-proclaimed Traditional Witch Roy Bowers, a.k.a. "Robert Cochrane", famously stated that witches were no longer witches when they were "pagans". There has been a good bit of confusion about this, but it’s really very simple to clear up.
For a man who wouldn't have considered himself a "pagan", Bowers and his "Clan of Tubal Cain" spent a lot of time praying to Hekate, "The Lady", "The Master", Tubal Cain, and others. They believed in "Old Fate", practiced sorcery, and Bowers may (if I am reading the accounts correctly) have considered himself an incarnation of a Sacred King figure.
Bowers was a Pagan, in every real sense of the word, and he was a sorcerer. I believe that he didn't consider himself a Pagan for two reasons. First was his bitter feud against Gardnerian Wiccans, against whom he coined several nasty names, including the name that would go on to become the ancestor of "fluffy bunny". The Gardnerians did consider themselves to be descendants of the Pagan witches of the past, and were clearly "Pagan" in their aesthetic. I imagine that his original rebuke of the word was born in this very conflict- and how this curse is far from dead! The second reason is because I believe he considered "pagan" to mean "uneducated" and "unenlightened", for indeed, that's how all educated people thought about the word "pagan" before the rise of the modern Pagan religious movement.
Cochrane was especially concerned about the Mysteries- he saw his "Tubal Cain" craft as a Mystery Tradition, aiming at wisdom and illumination, not merely spells or fertility rites. In this sense, Cochrane's craft operated on a higher "arc" than Gardnerian craft, which is still to this day concerned chiefly with fertility. The Gardnerian "supreme mystery expressed in ritual" is, after all, the "Hieros Gamos", the "Great Marriage", the ritualized act of male-female union. It is carried out through a sexual act, whether an actual one or a symbolic one, between a man and a woman in a circle.
It's easy to see why Cochrane would scoff at such a thing; while there are many important mysteries involved with the ideas and realities of sexuality, coupling, the marriage of heaven and earth, and fertility, those things aren't the beginning and the end of all the Mysteries. One is forced to wonder to what extent "fertility" dramas are really needful in the modern world with its burgeoning population.
Cochrane considered a witch to be a person who was a cut above the "common" mysteries of the rural, uneducated Pagan- the witch was the person more deeply initiated into recondite mysteries that would confound the common "salt of the earth" person. "Witches" to Bowers were people who had the power and courage to leave this world and travel into another, all to discover wisdom. In many ways, his distinction between "Witch" and "pagan" might be compared to the difference between "Shaman" and "non-shaman tribe member" in a tribal society today.
There is an element of anachronistic elitism operating in Cochrane's words; he was a product of his times, and very much a genius of the mystical arts. We can consider him a "Pagan" today, but only using our modern (or perhaps reclaimed) understanding of the word "Pagan".