Episcopalian
Episcopalian comes from the word episcopal, derived from the Greek word epískopos, meaning "overseer" and from which we get the English word bishop. It may refer to one who is a member of the Episcopal Church or the form of church government (polity) found in the Episcopal Church.
The Episcopal Church is a member of the worldwide Anglican Communion, the churches around the world that trace their roots to the Church of England, and maintain a “communion” with it, hence the name “ Anglican.”
Episcopal church polity
In general, episcopal churches are those with bishops that adhere to an episcopalian type of church governance. In the more specific sense the term is applied to those particular churches associated with the Church of England and Anglican churches.
The word "episcopal" is commonly used to distinguish between the various organizational structures of Protestant churches, thus the word presbyterian is used to describe churches ruled by elected Elders (Greek presbuteros) while "episcopal" is used to describe churches ruled by bishops. Others are neither, being congregational and local in structure.
Other churches overseen by bishops, with a connection to the Church of England yet not members of the Anglican Communion, include the United Methodist Church. All Methodist churches have their roots in Anglicanism because their founder, John Wesley, was an Anglican priest in England in the 1700s. Wesley held that bishops are merely presbyters (elders) who have been chosen for a supervisory position by the Church.
Churches that are members of the Anglican Communion are episcopal churches in polity, and some are named "Episcopal." However, some Anglican churches do not belong to the Anglican Communion, and not all episcopally-governed churches are Anglican. The Roman Catholic Church, the Old Catholic Churches (member of the Anglican Communion), and the Eastern Orthodox churches are recognized, and also their bishops, by Anglicans.