So is there a difference between Paganims and Wicca?
That turns out to be an enormous question...
The shortest answer is that Wicca is a denomination of modern Neo-Paganism.
Prior to 500BC (roughly) pretty much all religion was Pagan. Around 500BC all over the world there was a major shift to monotheism from polytheism, and most of the religions from the "world's N great religions" came from this time, and many of the leaders of major religions came from this period, such as Confucius, Lao Tsu, Buddha, several high prophets of Judaism, and more. So after 500BC many areas of the world became non-Pagan or mixed.
For us in the alternative community, the major religious alternatives tend to sort themselves into three groups: Paganism, NewAge, and Christianity. Paganism draws its inspiration from the "paleo-pagan" religions prior to monotheism, Christianity from Jesus (occasionally made Deist), and New Age (from Plato and Neo-Platonism and similar religious movements slightly prior to Christianity).
Few people in the alternative community know enough about Christianity to realize how much it influences them even after they supposedly reject it. Few realize that there is much more to Christianity than Fundamentalism (which only started around 1910). Our founding Fathers were Deists, and many of us who take all those "Find your Religion" tests online are surprised to see "Liberal Protestantism" listed high up. Liberal Protestantism, though getting little press coverage, is a powerful influence since it is spread by most of the major Christian schools of Theology, such as the Chicago School led for many years by Mircea Eliade. It is much like a blending of Christianity and Advaita Vedanta Hinduism and is VERY well-represented in this country even if very quiet relative to the Radical Religious Right (or Reich).
And even fewer self-professed Pagans realize that in their beliefs they may be more New Age than Pagan, and this includes many Wiccans. New Age, at one time termed "the Perennial Philosophy" starts with Plato, then Plotinus and the Neoplatonists, mixed with Gnosticism, Hermeticism, and the Mystery Religions, with a great debt to Advaita Vedanta Hinduism both early and later, was passed down through the Templars and various heretic groups, the Freemasons, Rosicrusians, Theosophy, to the Golden Dawn and the High Magickal traditions, until it informed much of Wicca through Gardner.
The Perennial Philosophy sees an essentially dualist reality with the world as an imperfect expression of the Divine Oneness, with our goal in life to achieve insight into the One and realize that we are one with the One. You realize you are dealing with New Age when you hear, "Many paths, one goal" or "all the many goda are merely expressions of "The One".
And Paganism is NOT merely "anything except Christianity". The actual Pagan religions with their 50,000 years of history have their own special traits in common with each other that are not Christian or New Age. Paleo-paganism pretty much died out in Europe (except pockets in Lithuania and maybe Iceland), but is surviving if not thriving in Native Americans here, in Central and South America, Africa, and parts of Asia. But again, they get very little press. And they can still inform we Neo-Pagans.
Neo-Paganism has become less Wiccan over the last several decades. Some of the major groups are:
Wicca: Starting with orthodox Gardnerian and Alexandrian Wicca which drew from the High Magickal traditions of Freemasonry and the Golden Dawn and such, now much is eclectic, taking from any number of religious traditions.
Witchcraft: Drawing from FamTrad, "family traditions" that have been passed down, low magic. (Before Neo-Paganism became popular and accepted, these folks called themselves "Christians".)
Reconstructionists: Those attempting to recreate the lost paleo-pagan religions of Europe which were wiped out by Christianity. Includes Asatru, Celtic (Reconstructionist|Restorationist|Traditionalist), Greek and Roman Reconstructionists, and many others. They spend much time in academic pursuits, using archeology, searching for remnants in literature, learning the languages.
Eco-religionists: Gaia, etc, seeing the earth as sacred, and worshipping through political action.
SciFi: Church of All Worlds (Green Egg, Tim=Otter=Oberon Zell), drawing from "Stranger in a Strange Land", treating modern science fiction as sacred, equivalent perhaps to a Book of Shadows... Started out right here in St. Louis before moveing out west...
And many other groups are loosely affiliated, such as the Rainbow People, the Science Fiction community, some SCA and Rennaissance folk, even some Satanists.
And so, in long, as the differences between Paganism and New Age start to become clearer after decades, Wicca seems to be an intermediary tying the two together.