I for one am very enthusiastic to say the least about the Meaning, Origin, and Correct use of terms. In particular where Magic is concerned.
Definitions in particular are important in the "Modern" Pagan Community. As an example Pagan, Witch, and Wiccan are not synonymous. A Wiccan is a person initiated into a Specific Religion. Wiccan Traditions are as an example but not limited to Alexandrian, Gardnerian, and others.
A Witch is someone who practices any number of forms of wise craft, healing, herbalism, and Spells to effect change in their lives and the lives of willing others. A Pagan loosely defines the the first two and any other person outside of the Abrahamic Religions of Christianity, Islam and Judaism. By the frame work of these definitions a person can be a Witch and still be Christian, but not Wiccan. When I say I am a Wiccan 2nd Degree I mean I was initiated as a Second degree in a Wiccan Teaching Coven. I am also a Witch and practice Spell work to effect Change in my life and the Lives of others who ask me to do so.
As Pagans we are reclaiming aspects of religious beliefs practiced centuries before Christianity, but as a Wiccan I am practicing a "Religion" founded in the middle of the 20th century maybe late 19th at it's oldest.
For what it is worth according to the Catholic Definition I am a Heathen not a Pagan. I was raised Christian and do not practice that faith. I am therefore a Heathen, to them Pagans have never been introduced to Christianity.
I base these definitions on the research and work of others before me not on Opinion.
here is a link to one of the references
http://wicca.timerift.net/
and another
http://davensjournal.com/index.htm?TOC.htm&1
It is also imperative that the "Burning Times" Myth be confronted at every opportunity. Wicca did not exist during the Inquisition, the numbers of people executed are over exaggerated, and many of the people executed were in fact Christians not even Witches. There is no Historical evidence to suggest otherwise. If you have it please present it.
You may ask what the point is in all of this well it is this, Frame of reference when having a discussion with one of you I now have given you a Frame of reference about the definitions I use. I realize this may even offend some of you but these are the definitions that seem to be common consensus.
Words have Power, due to their Meaning and Context, In Spellwork this is more exacting than many realize.
Blessings
Bear

I think it depends on where you get your information, or where the person is from who is giving you the info, when they got the information.
I learned, about 30 years ago that Pagan is the umbrella term for almost all people who most would consider Pagan.  Wicca, Alexandrian, Faery, Gardenarian, Eclectic, Green Witch, Kitchen Witch and more are all different traditions.  They are all considered Pagan. Most people now use the term Wicca (Wicccan) as the umbrella term.  
In the area I am in, where we have quite a few Wiccan and teachers who have been around for 25 -30 years, feel to be Wiccan, one needs to go thru Wicca classes and be initiated.  Now some are starting to use FamTrad or Family Tradition Wicca to define that they went thru the Wicca classes and were initiated.

Wicca is in and of itself a Religion within our "Community" A Wiccan is a person who Practices the Religion of Wicca. It has clearly defined parameters. Moreover it has specific Requirements of it's followers.

Ok. The people I know use Tradition. It's what I learned.  
It's ok.

Dosent the biblical quote of "suffer not a witch to live" sort of shoot that down? Although i guess that its more of a reference to Christian view of witches (pawns of satan etc etc) rather than the outline you defined above (but still this would be classified as witchcraft anyway by most christian authorities).