So when someone asks me is my personal heritage part of my Witchcraft, my answer to 'would my heritage (Polish) be part of my Witchcraft (British)' would be 'of course not' (being that I see Polish and British as significantly different) would be “heck, no.”
Now, granted, in the early history of Gardner’s bumping to Wicca, he was recognized by the New Forest Coven for being a descendant of Grizzell Gairdner. Obviously these Witches thought the blood was of some import. I don’t know enough to say if I thought they were talking about Witchcraft or a particular family’s version of Wicca, but I do know one hereditary Witch, and he would agree with blood being important; and not just 'related' but 'are you of the family' and it was pretty strict. You were either 'in' or you never heard a thing. And marriage was not enough, generally. The kids would be taught, but usually not the spouse.
So, for me, my Witchcraft is pretty much defined by what I’ve done as a Gardnerian, because other than some minor reading and exploration, that's the only training I have in Witchcraft or Wicca. Now if you ask me is that the extent of my Shamanic practice I would say 'heck, no' - I was taught by a Lakota woman, an Anishinabe woman, did some work with the hereditary friend, and learned some from local spirits (including the one I live in now). Some I got out of books, tried it, and found that it worked. Some I got from funky New Age workshops, but never had a decent context for it [i.e. I could 'do stuff' but there was no culture to tell me what was appropriate, etc.] until I became Gardnerian. The Gardnerian template has served as the uniting framework within which I utilize all of my shamanic learnings and explorations.
So why did I chose the labels I did? After all it’s not the way everyone uses the words. I think that for some people (for me) the narrowing of the definition of Wica is done out of respect; think about it this way: Here is a British label that is applied (mostly with negative associations) all over the place. Yes, unfortunately the same can be said of the word "Shaman" I mostly chose it (between the two; I haven't found a good third choice) because it's used in similar ways AND [key point] I don't know of anyone practicing a tradition with a historical context and cultural continuity that is currently calling it Shamanic; or at least I don't seem to run into them yet.
Frankly I'd love to find another word to mean "Cross cultural dealing with the 'small gods' and local energies and using magic and psychic abilities for the good of the local community". Right now I'm using shamanic for that.
And partly I latched onto it because my sis-in-law, in working on her doctorate, had some classes in comparative religions and urban shamanism, and that seems to be the word that is currently being tossed around in academia. Odd side note, she came out, visited us (pre-initiate stuff) and wrote us up as part of a paper - man do I actually look coherent on paper - not very realistic in my opinion, but flattering as heck.
There are cognates to how I use the word Witchcraft; the Russian 'viedma' the Nordic 'vitki' the Welsh 'gwyddon’ and so on.
In theory, I would be following the path of my own blood. Unfortunately, I’m third generation American Polish, and the first American born generation was really really really interested in being AMERICAN. The only cultural continuity I have with Poland is what I eat at Easter (which technically, I don’t celebrate any more, so there goes that).
Gardner himself was exposed to shamanic practices from multiple cultures; but the gods he related to (as I understand it anyway) were the ones that touched on his heritage/bloodline. Now as someone pointed out with the 'creating a new Sabbat' example, that does not mean other deities/spirits/totems [choose your term] are excluded, but it does mean (to me) that I understood my Gardnerian priesthood to be primarily an allegiance to those British deity forms/gods/spirits [again, choose your term].
I’ve heard that In the UK and Australia, the common practice is to use Deity Names that are common to the area as 'genius loci', and though it’s something I can understand, it's not the way I'm comfortable - specifically I'm not comfortable doing Gardnerianism that way - on the other hand the gods can invite other gods to circle, and I'm happy to meet guests.
I'll concede instantly that many deity forms can be seen to be cognates of each other (there are tons of hero gods, sky gods and so on). In that sense I think they represent different expressions of the same energy.
Just as human beings, are extensions of energies, and ultimately we are all connected. But I don't ask my sister if I can go over to my mother's house and borrow her stuff. I talk to my mother about that.
So if I have a relationship with a dying-on-the-cross god, and a relationship with a dying-grain-harvest-god, I can see that they are representative of similar base energies. However I think it's just rude to confuse them.