As a solitary witch coming from a long long line of celtic wise woman seers and prophetesses, I'm never quite sure about all these faith terms anyway.
I come from a basically christian background but at various times have also embraced Hindu, Buddhist, Dao, pagan, and various other beliefs in my spiritual practice.
I sort of regard being a witch as an esoteric life calling operating on the level of my spiritual essence, and which one can express using a variety of different exoteric religious principles and rituals. I "AM" a witch - but I can "believe" in many different faith systems (if you get the distinction).
For some reason it was the fact that I seemed to have inherited the family "gift", which by tradition passed only to daughters, that I think did the most to convince my mother and grandmother that there was something real going on when I was growing up. (Although personally I'm not sure I would want to put too much emphasis on all that stuff, but it kept them happy, so I'm not complaining.)
I'm not sure where that places me as regards to spiritual categories but anyway I just thought I would add my support to y'all!