Maturity, dedication, willingness to learn and study and willingness to be honest with yourself and others are some of the things that are important in Wicca. Now, most established covens and study groups will not accept any members under the age of 18. So if a minor's parents don't want him or her learning about Wicca, then anyone who taught it to him or her could get in serious legal trouble. But I always recommend that new Wiccans study and learn by themselves for at least a year, and preferably longer, before they even consider joining a coven anyway. That's kind of like asking what the difference is between Baptists and Christians.
Paganism is a word used to describe a very broad range of beliefs.
Wicca and other forms of the Craft are sort of denominations of Paganism. In other words, most Witches are Pagans, but not all Pagans are Witches. Some Pagans follow Asatru or Druidry or another religious path. You won't find us passing out tracts on street corners or knocking on doors spouting sermons. Wiccans do not try to convert others to their faith because we believe there is more than one path to the God and Goddess.