Wiccan or Witch?

You can be both a Wiccan and a witch, these two words are not the same
One of the biggest sore points among Wiccans is the improper usage of the terms "Wiccan" and "Witch". Too many people use the terms interchangably, presuming that they both mean the same thing. They do not.

Wiccan
Wicca is a religion, and someone who follows that religion is called a Wiccan. Sometimes it can be difficult to accurately define Wicca, and not all Wiccans will define themselves the same way. Observing the 8 Wiccan Sabbats, honoring the Gods and/or Goddesses, creating sacred space for rituals, to name a few. Many traditional Wiccans also feel that belonging to a coven is also a requirement and that those who practice their religion as a solitary, should not refer to themselves as Wiccan. Personally, I'm still not sure on that point. Typical Wiccans also practice magick, and therefore are also witches.

You cannot be a "natural Wiccan" any more than you could be a "natural Christian".

Witch
The practice of witchcraft is not associated with any religion, therefore you can be a witch and yet also be a member of any number of religions (or none). Using the natural energies within yourself, along with the energies of herbs, stones or other elements to make changes around you is considered witchcraft. Though the skills and gifts that are part of witchcraft can be inherited from parents or grandparents, you aren't automatically a witch just because your grandmother may have been one. The use of magick takes practice, experience and learning. On a side note, a male witch is called a witch, not a warlock.

Pagan
While I'm explaining terminology, I thought I would throw in "Pagan" as well. Paganism refers to a variety of non-Christian/Jewish/ Islamic religions that are usually polytheistic and are often nature-based. Wicca is only one Pagan religion, but there are others such as Santeria, Asatru, or Shamanism. Many people do not necessarily identify with a specific religion, and just use the broad term "Pagan" to define their spiritual path. Pagan religions are distinct and separate from each other, and it should not be assumed that they are just different names for the same faith.