As discussed previously, Western religious conflict has a long history. Conflict between the emotional side of religion and the rational side appears on more recently, too, in small, new traditions without the history and numbers of the Christian faiths. In the 1800s, the Romantic movement, rebelling against the science that brought the Industrial Revolution, retold the history of the witch hunts of the pre-Enlightenment period as a sad tale of poor, misunderstood pre-Christian people persecuted by evil and unemotional church bureaucrats. In the 1900s, as the wars of the early 20th century raged across Europe, this anti-scientific progress sentiment arose again, and small groups of people began meeting in covens, creating an entirely new religion out of the Romantic imaginings of the anti-Enlightenment artists. These were the beginnings of the neo-pagan religions.
There are a large number of sects and subdivisions in the category of neo-pagan religions, and yet they can be categorized in many of the same ways as more established faiths.
Publicly, Wicca can be traced to the 1950s, when Gerald Gardner published his book, Witchcraft Today, as a pseudo-anthropological look at witchcraft celebrants of his acquaintance. It has what is likely the most direct connection to the Romantic and Victorian era occult fascination, yet early practitioners often insisted that they were celebrating rites that had been passed down generation by generation from authentic European witches of the 1400s. Modern Wicca draws upon this tradition: although celebrants now are less likely to claim a direct family inheritance, many still believe that their religion is a remnant of pre-Christian pagan practices of the Middle Ages.
In addition, common elements of the faith have roots in varying mythologies, and often reflect an open attitude to adopting whatever feels right from other cultures. Mother Goddess may be Roman, Egyptian, Sumerian, Greek, or Celtic, but the division of sacred space - the circle - is always into 4 quadrants, usually assigned to the elements earth, air, water, and fire in a haphazard fashion. (generally, north=earth/east=air/south=fire/west=water, although variations occur.)
After the emotional side of religion had about a 10 year head start, it started drawing a different kind of seeker: one who was seeking wisdom, but who had the education and rationalism to recognize that the myth of the family tradition handing down witchcraft over 5 centuries was hogwash. One who recognized the value of the work being done in archaeology and anthropology to find the actual pre-Christian peoples of Europe - much farther back than 500 years - Stonehenge as we know it is approximately 4000 years old, and there is evidence that humans had been using the site at least 1000 years before that. These seekers created a historical recreation branch of neo-paganism, and their legacy is seen in groups and people such as Ár nDraíocht Féin, Nova Roma, Numinism, many Asatru, and IMBAS.
I might say that there is a cordial relationship between the two different branches of paganism - by and large, neo-pagan Wiccans who are building traditions on heart, adopting what "feels right" whether it comes from the same mythology as their chosen deities or another, often don't know that neo-pagan reconstructionalists exist. Neo-pagan Reconstructionalists are aware of Wiccans in their area, and respond individually - sometimes avoiding contact, sometimes inviting them to take part in a reconstructed ritual. By and large, though, it appears to be two different worlds, tied together on paper only by a similarity of mythology - very much as the evangelical and legalistic Christian churches appear to be two separate worlds, separated by a belief in the best way to hear God.