Well, no.
There are … what? … Native Anglicans - that is, ecclesiastical sons of the English Reformation who reside in the United Kingdom - who have no communion with the State Church. They’re called The Free Church of England. They are Protestant, reformed, and date from a low-church evangelical reaction against Oxford Movement efforts to pretend that the Reformation didn’t happen (or, was just a momentary aberration).
Originally, much (maybe most?) of the American colonists were Anglicans. After the Unpleasantness dating from 1776, those same Anglicans found they had won a political war against their ecclesiastical head (King George). What now, ecclesiastically, that is?
First, they decided to call themselves Episcopals or Episcopalians, denoting that their church was ruled by bishops. Anglican, you see, is just a Latinesque word meaning “English.” So, we were now Episcopals.
Except American colonial Episcopals had no bishops! And, in Episcopal polity, only bishops can ordain new priests and consecrate new bishops. So, Samuel Seabury heads off to England, where the English bishops tell Seabury to pound sand.
The non-juring Scottish Church, happy to poke a finger into ecclesiastical eyes down south, consecrated Seabury and sent him back to the colonies.
Fast forward a couple of centuries, and the Episcopal Church in America was terminally apostate, shedding parishes and dioceses all over the place. Episcopal at this point meant (and still means) pro-abortion, pro-homosexuality, pro-ordination of women to the presbyterate and episcopate, and sundry other heretical thangs. So, those departing the Episcopal church don’t want to call themselves Episcopal any longer. What to do?
Most of us now revert to calling ourselves Anglican, not because we wish to be part of the modern English state church, but because we wish to indicate “We’re not with them” (while pointing to those Episcopals) and also to signal that our roots are in the English Reformation - the one claiming Bishops Cranmer, Latimer, and Ridley as martyrs.