This is a slightly tricky question, but I'll give it my best.

To begin with, no, historical European witchcraft does not relate to present-day Wicca. Wicca is more a new twentieth century religion that combines alleged ancient knowledge with new discoveries—it has no relation, really to historical 'witchcraft'; it has some connection to Theosophy, at least in terms of philosophy.

As far as European witchcraft, I honestly can't think of much better a term than 'thought police' in a sense: the early Christian church, including on down through the ages, was filled with a variety of different interpretations of scripture. Those who did not subscribe to the orthodox interpretation or that believed in a different belief system altogether often were categorized as demonic or involved in witchcraft. Though this came to a head around 1100, this can even be seen with the early Gnostics, Valentinians, and St. Augustine's incorporation of sort of dualistic beliefs into his readings, likely a result of his time spent as a Manichaean hearer. Per Witchcraft in Europe 400-1700:

Some elements of witch beliefs, of course, antedate the period of pandemic fear and active persecution, roughly from 1430 to 1660. Historians of late antiquity and early medieval Europe, folklorists, and anthropologists, in fact, have long debated the exact sources from which they were drawn and the diverse methods of their continuing existence. Celtic and Germanic religion and folklore, bliblical and patristic speculation on the nature of evil, Neoplatonism and the related philosophical and subphilosophical spiritualism of late antiquity, and even the postulated survival of "underground" ancient pre-Christian cults have all been identified at one time or another as major contributors. ...

From 1100 on, however, indistinct and often idiosyncratic strains of belief were organized in wester Europe into an increasingly coherent and generally uniform system of theological and juridicial dogma, the logical implication of which was the obligation of churchmen and their secular courts actively to seek out and extirpate the witches and their protectors and defenders. ...one can trace the transformation of individual sorcerers, shamans, and "cunning" men and women [folk medicine practitioners] of earlier centuries into the diabolical sorcerer and witch of the period of persecutions. ...

Before 1100 or so, churchmen generally professed skepticism concerning the alleged activities and magical powers of witches.... Churchmen, after all, by 1100 had virtually disarmed the last bastion of pagan beliefs by convincing men and women that "the gods of the pagans were demons in disguise," that all pagan religious practices (whether Mediterranean or northern European) were superstitions (a much stronger word then than now), and that some pagan religious practices constituted forbidden magic. ...

Many contemporary observers from the fourteenth century on looked upon manifest diabolical sorcery and witchcraft as quantitatively and qualitatively the single greatest threat to Christian European civilization. ...In the sixteenth century Protestants accused the Roman Catholic clergy of fostering witchcraft through "popish blasphemies," and Catholics in turn proceeded to identify witchcraft, first, with traditional and recognized heresy and later with Protestantism itself.

Around this time, in essence, what is considered witchcraft is systematized and categorized. An example of this can be seen, for example, in the Albigensian Crusade, where the Cathars were hunted down by the Catholic church in spite of being a fellow Christian sect, because they were conflated with witchcraft and errant beliefs. The Cathars were a dualist sect (believed in gods of good/evil and that the physical world had been created by the evil god) that had evolved from the earlier Manichaeans.

The major Christian attack on the pagan gods had anathematized them as evil spirits who deluded mankind. The systemization and elaboration of these beliefs beginning around 1100 gave the myriads of sub-demons an essential place in the development and ideas of witchcraft. ... In the increasingly systemic thought of [Thomas] Aquinas and his contemporaries, however, folklore became complex and rigorous ecclesiastical doctrine. The demons were evil angels who had the ability to unite themselves to bodies and to communicate their knowledge and commands to men and women. They were a hierarchically organized army in the service of Satan working collectively for the perdition of the faithful. They also could secure both present and future service by written contracts with humans, leave distinguishing marks as tokens of that service on the bodies of their human servants, gather their servants into nocturnal assemblies called "sabbats" to pay homage to the devil and plan new assaults on the human community, have sexual relations with humans, and give humans the powers of flight and morphological chance. Such human servants of Satan became the witches of the theologians and inquisitors, the visible agents of demonic power. Once the diabolical sorcerer or witch had come to be understood in this new context, the logic of witch-hunt and execution of the convicted sorcerer or witch became manifest and compelling. There could no longer be simple superstition or simple magic performed by self-proclaimed cunning-folk, wizards, wisewomen, or magicians, even if such rites were aimed to relieve human suffering and anguish—there could only be the diabolical sorcerer or witch.

In addition, after 1100, most emphasis in religious belief is placed both on Christ's suffering and on Satan's insurmountable power—which leads to the belief that humanity is helpless without God against the powers of the devil. As time goes on, the excuse of witchcraft comes to be used to silence both religious and social rebelliousness: if you believe anything other than the orthodox beliefs, or consult any of the folklore of your youth, you have been touched by the devil or possessed.

Socially, this can be seen in such environments as Salem (not European, admittedly, but still a valid example): most often, the women targeted were either social outcasts, had more money than was considered appropriate for a woman of the seventeenth century, or had otherwise transgressed on social norms. Boyer and Nissenbaum reinforce this by pointing out that more often than not, those accused of witchcraft in Salem lived on the other side of the village from their accusers and were likely to be defended by their nearby neighbors, indicating a social conflict.