Over here, the Anglican Church, as the Church of England, is the state church. It, broadly speaking, can be divided into liberal, Anglo-Catholic and evangelical portions; unusually, perhaps, all three branches tend to have some form of social justice/ social gospel aspect. But in addition the three branches tend to have the following individual characteristics:
Liberal - the most traditional form typically, bearing the most allegiance (even if only on paper sometimes) to the 39 Arts and the 1662 Book of Common Prayer. Tend to wear vestments (but not Roman Catholic-type ones). On communion, they would tend to be Cranmerian receptionist ie: we spiritually receive Christ's Body and Blood when we take communion. OK with infant baptism. Also theologically, they would tend to subscribe to higher critical theories re Scripture and not have a problem with same-sex relationships or women priests. Heroes of this tradition include Lancelot Andrewes, Richard Hooker, Thomas Cranmer (possibly), William Laud (to an extent), the present Archbishop of Canterbury, ++Rowan Williams, and, more on the extreme, +John Shelby Spong and +Gene Robinson.
Anglo-Catholic - "more Roman than the Romans". Have their roots partly in the Laudian reforms of the 1620s and 1630s but more importantly in the Tractarian Oxford Movement of the 19th century. Big emphasis on Apostolic Succession with Anglican bishops, priests, being rooted in the Early Church and Early Church Fathers, and view the 39 Arts as more or less compatible with Roman Catholicism; they see the Anglican Church as sister Catholic Church to the Roman Catholics and Orthodox. Much more Catholic-style 'tat': vestments, incense, candles, statues/ icons, Virgin Mary etc. Against women priests (many of their clergy swam the Tiber after the 1992 decision to ordain them). Divided on same-sex relationships (the Anglo-Catholic group Forward in Faith is opposed but Affirming Catholicism is pro-). Fine with infant baptism. Believe in some kind of Real Presence in communion although unclear as to whether actual transubstantiation. Heroes: William Laud (to an extent), John Henry Newman, and ++John Hapgood, previous Archbp of York.
Evangelicals - much more numerous over here than in ECUSA. Believe in salvation by faith alone, the need for personal conversion, supreme authority of Scripture, and other usual evo stuff etc. Many are Reformed/ Calvinist and tend to stress the Reformed aspects to the 39 Arts. Less sacramental and sacerdotal than the others, but still wheel out a priest (often in plain-clothes) to do communion, which they tend to regard as receptionist (or memorialist in a few cases); divided on infant baptism and tend to encourage believers' baptism. Against same-sex relationships. Divided on women priests. Heroes: Wilberforce, Ashley Cooper/ Shaftesbury, Jim Packer, ++George Carey, previous Archbp of Canterbury and ++John Sentamu, present Archbp of York
I can do links to the various Anglican groups if anyone's interested...