Wicca is an Modern Earth religion, with as many interpretations as Christianity. It is a religious form of Neopaganism, a mixing the beliefs of the Ancients both urban and rural Pagan traditions. There are generally held beliefs, but individual experience of the Godhead in Nature, often in the form of an Earth Mother / Goddess, often but not always accompanied with her male concert, The Horned God. Humans have control and responsibility over their destiny, but can be assisted by recognition and activity worshiping Nature. The morality is summed up in the Law of Three, that which you do returns to you three fold, good or bad, and the Wiccan Rede "As ye harm none, do as thou will".
When WITCHCRAFT was revived in England by Gerald Gardner, one of his main rivals was Charles Cardell. After an early schism from Gardner's Bricket Wood coven, he founded the Coven of Atho. He called his practitioners "Wiccens" or Wise ones. He was big into Welsh (not Gaelic) culture, so...might have been his understanding of Wise in that unusual dialect.
In the 1960s, we Americans were still calling it Witchcraft, following the books that came our way, some by Doreen Valiente, Charles Leland, Margaret Murrayand Robert Graves which still called it Witchcraft.
Indeed, the 1st time I heard the term was from Leo Martello, a Pagan activist in the 1960s NYC magical community. Even though his books still used the term Witchcraft, he started using it long before forming WICA, AKA the Witches International Craft Association.
By the early 1970s, the term had caught on in America, and began to replace the old fashioned "persecuted heathen" term Witchcraft with it's anti-Christian connotations with this more modern term. Writers such as Starhawk, Margot Adler and practitioners such as Judy Harrow helped define and express this new religion, and emphasize it's diversity.