The Church of England is the official Christian church of England. It was established by King Henry VIII when the Pope refused to allow the annulment of Henry's marriage to Catherine of Aragon so that the king could marry Anne Boleyn. The Church of England follows practices of both the Catholic and Reformed churches.
The Episcopal Church was the outgrowth of the Church of England in the American colonies with the first church founded in Jamestown in 1607. The Anglican Church [CofE] dominated New England, New Jersey and New York during the Revolutionary Era. Anglican ministers had to swear allegiance to the Crown in order to keep their positions.
In at least one case, residents of Hunterdeon Co., NJ understood the minister's predicament. They had had their children baptized in the local Anglican Church while their Presbyterian Church was being rebuilt. They hung the the minister in effigy, but otherwise left him and his church alone.
Other than the handful of Puritans, Pilgrims and members of other denominations already discussed my New England ancestors were Anglican. Of note, the Simmons family of NYC attended Trinity Church in New York City and, to the best of my knowledge, the family continued to follow the Episcopal/Anglican faith into the 20th century.