The churches most familiar to me that use "Episcopal" rather than "Anglican" in their names are the US and Scotland. In both cases, there were times in our history where we and England were mad at each other, and choosing a name other than "Anglican" gives a little distance from England. (Here in the US, we've long since made peace with England, though we never joined the Commonwealth. I'll let the Scots answer for themselves.
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As to the original question: "Anglican" is the name for the broad theological / ecclesiastical tradition coming out of the English Reformation, so the Episcopal Church is part of this. If you'd asked me 30 years ago, I would have used the terms "Episcopalian" and "Anglican" roughly interchangeably, and that's still correct wording. More recently, though, in the US the term "Anglican" tends to be heard as referring to the ACNA and similar bodies. With that in mind, I now use the label "Episcopalian" most of the time, to clarify my views on a collection of theological issues.