Well said said everybody.
It is a widely held belief that all Witches are Pagans, but not all Pagans are Witches. Wicca, like Witchcraft, is a specific path under the umbrella of Paganism or Neo-Paganism.
Some believe Pagans are not all similar, any more than Christians are all similar. The general beliefs, practices, politics, and lifestyles of Gardnerian Wiccans are not the same as Asatru, etc. Ed Fitch is not Lori Cabot , etc.
Wicca by design IS a religious tradition with real, hard and fast rules. However, Wicca as a religion is becoming DILUTED from its original British Traditional origins into a "if it feels good do it" blend of Eclecticism commonly referred to as Neo-Wicca. Many Traditional Wiccans, sometimes referred to as "Old-Guard," continue to hold onto their hard rules, and are often branded as "Orthodox," "Fundamentalist," or "Conservative" whenever they speak out against the "Eclectization" of Brit Trad Wicca. Or they do not speak out at all, which I believe is a true shame.
It is a hotly debated issue within the Craft Community. Most Traditional Wiccans keep to themselves because of it and do not wish to participate in the discussion. The "hyphen-Wicca" groups which have appeared over recent years have driven many Brit-Trad Wiccans further underground, shunning the "limelight" and keeping to themselves and their Covens to protect their material from those who would steal it and publish it for their personal glorification or legitimacy.
Although there is a common thread between various groups or Traditions outside of Wicca, they do not necessarily subscribe to the tenets which are inherent to Traditional Wicca (i.e., Deities, ritual structure, procedures, etc.). In this regard, Druidic, Dianic, Seax, Pictish, Pagan and Shamannic Traditions technically are not Wiccan by definition. But then we go right back into the brain-killing semantics!
Essentially, the issue of Wicca can be broken down thus:
Traditional Wicca - is still kept secret (Oathbound), still practices initiation, does not accept self-initiation, and still teaches one-on-one after a certain basic level is reached. It has its own dogma, a uniform pantheon which is Trad-specific, it's own cosmology, and other lore not readily available to the "Craft Community" at large.
Hyphenated Wicca - this is anything that starts with the name of another culture, real or fictitious, then adds a hyphen and the term Wicca. Examples are Sumerian-Wicca, Eskimo-Wicca, Klingon-Wicca, Jedi-Wicca, Egyptian-Wicca, Cyber-Wicca, etc. Here, a very basic form of Wicca has names, phrases, titles, deities, etc. from another culture forced into it.
Eclectic Wicca - this is the strangest form of all. In Eclectic Wicca (what I call "Neo-Wicca"), all the teaching of Traditional Wicca (which is, after all, what this is all based on) are ignored, forgotten or have never been learned. Here anyone is practically free to create absolutely anything, make any claim, take any ritual and change it to something they like, and then pass it on as ancient wisdom. Eclectic Wicca does have its benefits, but is essentially a popular "fad," much the same way Spiritualism was a fad in the 1800s. Those following this path are responsible for the huge majority of books on the topic, are often badly researched, and even badly written. It is the fun of being Pagan without the work entailed in Traditional teaching and study.
Eclectic-Wicca is Paganism (not that there's anything wrong with that!).
I’ve also been seeing a lot of people inaccuratly refering to the Rede in this folder, so I’ve decided to include the following:
The Rede of the Wiccae is not "LAW." This is a fundamental misconception by many people not privy to the Oral Mysteries behind the Rede, which are Oathbound teachings given only to Initiates of the Tradition from which the Rede originated. The translation of the word "Rede" means COUNSEL. It is not, and was never intended to be LAW.
The Rede of the Wiccae is a classic example of how Traditional Wiccae material has been co-opted by many people new to the Craft scene without realizing the full implications behind it. I guess it's a tribute to the simplistic "Universal Truth" contained within it, but it also causes a great deal of confusion
http://www.witches-tutorial.com/paths/wvsp.html
So there has always been the question that you have asked, it would just depend on on what the person believes
