Anglican

'Anglican' only refers to the Church of England and churches derived from it - most of which are members of the Anglican Communion. 'Anglican Church', although often used as such, is not a synonym for 'Church of England'. Outside of England it is often used as the title e.g. by the Anglican Church of Canada.

'Anglian' could be used as the adjective for things English generally, but is in practice only used in 'East Anglian'.

Anglican - of, relating to, or denoting the Church of England or any Church in communion with it.
noun - a member of any of these Churches.

ORIGIN early 17th cent.: from medieval Latin Anglicanus (its adoption suggested by Anglicana ecclesia ‘the English church’ in the Magna Carta), from Anglicus, from Angli. http://oxforddictionaries.com/definition/english/Anglican

The wonted way is to note "anglo" by itself or with another word ... "Anglo-American" can mean UK-US relations.

Otherwise, if yu want to talk about England related things ... then note "English".

That should be about as clear as mud ...

Isn't "anglo" the shortened form of the word Anglican?
Like Hispano-American relations, Hispanic and American.

Perhaps in Anglo-Catholic, though that might have originally signified 'English' as opposed to 'Roman' Catholic.

But otherwise not.

Clarification... Anglo can not refer to the UK or all "British" and "Britain" because not all parts of the UK are "Anglo." Remember Anglo refers to the people that settled into the area of the British Isles that became known as the Kingdom of England - the Anglo-Saxons. That's the eastern part of the country. To the north were the Picts and eventually the Scots, to the west were the Welsh, in the kingdoms of, respectfully, Scotland and Wales. So when you see Anglo being used as an adjective prefix, as in an Anglophile, it means that person is studying specifically English history, which will include Ireland, Manx, Scotland, and Wales, after England conquered them all, but doesn't before that time of annexation or after such things as Ireland's independence. Hence the reason for calling the "Church of England" the Angl(o)ican Church as it was establish by the King of England, Henry the VIII for the Kingdom of England. When the church's congregation spread, especially to areas of the United States, which fought for independence from England they certainly were not going to call themselves the "Church of England" over here surrounded by founding father patriots of the country. At the same time the couldn't lie about who they were either, so they chose a different way of describing themselves abroad...the Anglican Church. There wouldn't have been a description for "Anglo-Catholic" because Henry wasn't looking to be Catholic. He was cutting himself and his kingdom from that faith entirely where he (and after him the ruling monarchs of his kingdom) were the head of the church not some other "governing" body that could pose possible threat to his authority or religious decisions.

But it is a fact that 'Anglo' is often used to mean 'British' for example in Anglo-American.

A couple of other points. England never conquered Scotland, and the American colonies fought for independence from Britain not England.

English History as an academic discipline would not (nowadays) include the other parts of the British Isles except in so much as they related to England.

'Church of England' is actually a translation of Ecclesia Anglicana - a title also used before the break with Rome. Henry VIII in doctrine remained close to traditional Catholicism and the doctrinal statements of his schismatic church (as one might call it) became more conservative as his reign progressed. The term 'Henrician Catholic' is sometimes used to describe the Church of England during his reign. Many modern Anglo-Catholics looked back to this period as a representative of their own position.

This reminds me of something from "1066 and all that", a gentle parody of history teaching in British schools by W. C. Sellar and R. J. Yeatman, published in 1930.

"Noticing some fair-haired children in the slave market one morning, Pope Gregory, the memorable Pope, said (in Latin), 'What are those ?' and on being told that they were Angels, made the memorable joke — 'Non Angli, sed Angeli' ('not Angels, but Anglicans') and commanded one of his Saints called St Augustine to go and convert the rest."

What the pope was told,of course, was that the children were Angles, and is reply was "Not Angles, but angels" - which perhaps gives us a clue where Anglo comes from - Angli, the medieval Latin name for the English .

Another "1066 and all that" translation: for "Honi soit qui mal y pense"- the motto on the Order of the Garter - they have "Honey, your silk stocking's hanging down".