One of the more frustrating parts of being a continuing Anglican can be deciding how to describe our tradition to Christians of other traditions. First there is the problem of "Episcopal" vs. "Anglican". Why can't people understand that the terms are interchangeable, but do not mean the same thing? It is like saying "Kleenex" and "Tissue". They mean different things, but they refer to the same phenomenon. Our tradition is ""Episcopal" because we are governed by bishops, and we are "Anglican" because we derive from "England". For some reason this confuses people. Usually I tell people that we refer to ourselves as "Anglicans" to differentiate ourselves from the mainline Episcopal Church, and that we wish to do so because of strong differences in certain beliefs. I then explain that it is technically okay for a member of ECUSA to refer to himself as Anglican, as well as for a member of the ACA to refer to himself as an Episcopalian. Again, am I explaining this in a confusing way? Are we Anglicans just so used to understanding all of this that we cannot fathom an outsider not understanding?
That's usually the biggest hurdle. Once that is cleared, I just go on and talk about being an Anglican. If they make some comment because they think I am in ECUSA I say, "Oh, I am not in the mainline Episcopal Church. I'm in a smaller, more traditional Anglican denomination called the APA. We are a completely different Church with our own heirarchy and structures." And if they ask I will explain some of the differences of belief, such as in the areas of ordination, BCP, sexual ethics, and so on. If I am talking with a conservative Presbyterian I say, "APA is to ECUSA as PCA is to PCUSA". Or, "APA is to ECUSA as LCMS is to ELCA." That usually lets people know that I am in a different Church than ECUSA. And then, of course, I tell them that there are numerous small, conservative Anglican denominations... just like there are numerous small conservative Presbyterian denominations. I don't like to have to resort to all of the denominationalism - I do not even like the word - but it does help simplify things a bit.
I think that it is important to differentiate ourselves from ECUSA when necessary. It is also important to remember that we can use the term "Episcopalian" and not be afraid. ECUSA does not own the rights to that word anymore than Ford owns the rights to the term "sedan". Americans know what "Episcopalian" is, so we should reclaim that term if we want to. But we are also free to use the term "Anglican".