tl;dr - No.

The idea that people persecuted during witch trials really were witches, or followers of some kind of cult, is called the witch-cult hypothesis and stems from Margaret Murray's 1921 book The Witch-Cult in Western Europe. She thought that in witch trial records she could find evidence of an ancient religion that predates Christianity and which survived right under the Christians' noses until very recently. This idea remains popular with certain Wiccan groups, but has been entirely discredited by scholars. No serious academic believes the people killed during the Salem Witch Trials were anything other than unfortunate individuals - certainly not real witches.

As for "witchcraft", it depends on what exactly you're talking about. Neo-Druidry and related movements, which heavily influenced the formation of Wicca, are a product of the late 18th century. That period saw a kind of druidic revival whose most influential figure was a Welshman named Edward Williams (he later changed his name to Iolo Morganwg). Morganwg was a hardcore Welsh nationalist, and he worked hard to publish old Welsh texts and anything he could find that he thought might be related to Druidry. He also organised groups with an explicitly religious character, performing rites that he had "re-created". Unfortunately he was also a fraud who invented many of the texts he published, and the religion he helped to create has very little to do with real historical Druidry. All of this was deeply bound up in the Romantic movement, and would go on to heavily influence Wicca.

Wicca really got its start with Murray's book. Murray believed that not only did this secret religion exist, but that we had vast amounts of evidence pertaining to its structure and practices. Witches formed covens, for example, which had 13 members, and there was a witch-priest dressed in animal skins at most or all meetings. None of this, I need to stress, is rooted in fact; Murray was taking "confessions" from "witches", many of whom had been tortured into saying what the courts wanted them to say, and which had been recorded across a huge range of time and geographical distance, and viewing them through a lens that everything they said was a) true and related to the secret religion, and b) that the secret religion was older than Christianity and not Satanic in nature. Her idea of the witch-priest in animal skins, for example, came from "confessions" in which the accused witches said that the devil was present at sabbaths.

But her ideas were hugely popular for a while, and they found an eager reader in a guy named Gerald Gardner. Gardner claimed to have been initiated into a coven in the New Forest, in England, and to be presenting the authentic teachings of that coven. He mixed Murray's ideas with some influences from Neo-Druidry and Freemasony, as well as some more contemporary influences like Aleister Crowley's school of magic. He and a few others were essential in bringing attention to the new faith, formulating some of its basic ideas, and spreading them abroad.

A very good book on all of this is Ronald Hutton's Triumph of the Moon.