Wicca, the religion as it is now known and currently called, is a practice that developed in the early half of the 20th century.
"The Wica" or "Wiccae" wikken, wiccian, etc. are terms born of old german, and possibly Icelandic Vikti or Vikta, which likely all influence the English witch. Interestingly, translating "Witch" into another latin-based language usually results in a word more akin to Sorcerer unless you are directly saying "Witch," in reference to a particular modern faith.
So to answer the root question, Wicca the religion came much later. Witch came first, and is perhaps born of the german/saxon word Wiccan(and various other versions of it).
As to arguements about the age of Wicca, the religion:
Wicca is less than a hundred years old, so...
Yes, even Christianity and Satanic practice predate "Wicca" and even paganism, as "paganism" is a modern adaptation of a word "pagan" created to describe polytheistic religion by Christians.
What we now practice is very new, as the practices generally deviate quite widely from the original methods of the ancients. These more modern methods of magical practice are more heavily influenced by and born within the occult study of the 18th, 19th, and 20th centuries (primarily), wherein the study of ancient and medieval magical practice and manuscripts become popularized among those who usually had a lot of money and time.
Yes, there are very deep roots that color what we now do, but when you get down to it we aren't living our lives or faiths like Druids, priests, and magi of ages old.
Now, I'm not saying what you practice is wrong, and I love the diversity of faith. I certainly think that stepping away from many of the old practices (like human and animal sacrifice) are steps in the right direction. I do however think it's important to know your history.