WHAT IS WICCAN?
The technicalities of how Billy Kaplan relates to William, son of Wanda & Vision, are complicated enough to merit their own section. Here we will discuss exactly what the twins were, when they were, and how they were.
The original story was that Wanda used the magic of an entire town of witches (while being held 
by her husband Vision) to bend the laws of probability to the breaking point and become pregnant. Sure enough, nine months later, she gave birth to Thomas and William. How? Descriptions of Vision's composition vary between mechanical or synthetic parts, but he is always artificial and contains no genes or DNA. No matter how improbable, what could Thomas and William even be made out of, beneath the skin?
John Byrne explained the situation by saying Wanda had actually experienced a hysterical pregnancy, a psychological condition where a woman wants children so badly her body convinces itself its pregnant and begins showing the biological symptoms of pregnancy. Wanda's situation went a step further, however.
The demon Hell-Lord Mephisto had been severely weakened in battle with Franklin Richards, his essence split off into five shards and scattered throughout the realms of men and mystics. Being the liar and manipulator that he was, Mephisto gave powers to a mortal named Martin Preston and claimed he had torn Preston's soul into five pieces. Thus Preston, as Master Pandemonium, became Mephisto's unwitting agent in hunting down his missing essence shards, believing they were parts of his own soul.
Wanda's spell, in trying to fulfill the conditions of her hysterical pregnancy, latched onto two of Mephisto's soul shards and used them to actually give birth, which is normally impossible in a hysterical pregnancy. Therefore, Thomas and William were born as animated aspects of Wanda's spell, bound to the soul shards. Master Pandemonium eventually claimed Thomas and William as aspects of his soul, only for Mephisto to claim them in turn. The twins and other soul shards were reabsorbed by Mephisto, Mephisto was banished, and the children were seemingly gone forever.
So then what?
Wanda, it seems, reincarnated her twin sons in the bodies of Billy Kaplan and Tommy Shepherd. According to the original Avengers: Disassembled story, Wanda had always been a supremely powerful reality-altering being. However, by Avengers: The Children's Crusade, this was walked back to her channeling the power of the Lifeforce only shortly before the events of Disassembled. Therefore, the reincarnation probably occurred during that short window of time. How exactly Wanda accomplished this is unknown. Time travel may be involved in some way, for Billy and Tommy were clearly older than William and Thomas. But did Wanda and the Lifeforce cast their bodies through time, or merely their spirits? Do Billy and Tommy share genes with Wanda Maximoff, or did the Kaplans and Shepherds give birth to their own children, merely with the migrating reincarnated souls of Wanda's boys?
One final question is whether Billy and Tommy are mutants. This was stated affirmatively once or twice back in the day, but at the time it seemed to be a presumption since their mother and infamous grandfather were mutants as well. Since the revelation that Wanda is not Magneto's daughter or a mutant, however, it becomes much less likely that Billy's powers come from an X-Gene. It is possible for non-mutant superhumans to have a mutant child, like Franklin Richards, but the presumption is no longer as strong. Although it was never specifically named, the Lifeforce Wanda tapped into was almost certainly the power of the Demiurge, the sentient biosphere of the planet Earth that created the original Elder Gods, and whom Billy is destined to replace in the Utopian Parallel timeline. Billy himself has also acknowledged that, while his powers resemble magic and are often manipulated like magic, they are not. He is a reality warper, having performed only a cursory study of the arcane arts, and draws his power from elsewhere. So while Wiccan is occasionally referred to as a mutant or a magician, in fact he may not be either.