What is the difference between "English" and "British"?

As an American, I naively think of British and English as exact synonyms. I know I'm wrong, but I just don't know in what way. I am vaguely aware that people in the UK hold strong opinions about one or the other term and how it is applied, and using one instead of the other has dire social implications.

So there is geography (Britain vs. England), but more importantly the adjectives British and English, and those adjectives each one by themselves, may mean different things in different contexts, and depending on the speaker and the listener.

Can anyone explain the nuances of the differences as used by those who might consider themselves English (or British, if that's an acceptable usage)? How about by the non-English/non-British (again if it's appropriate to use such terms).

(What I am not asking: I had to hold back from asking exactly what the distinctions among UK, British Isles, Great Britain, etc are as well as things like are people from Northern Ireland considered Irish (or do you call them Irish).)

Solution 1:

The country of which I am a citizen is the United Kingdom of Great Britain and Northern Ireland. Great Britain is the largest of the British Isles and is home to England, Scotland and Wales. I was born in England and, apart from several extended periods abroad, have lived my life in England. That makes me ethnically English and politically British. Although Great Britain is a geographical term, British describes nationals of the whole of the United Kingdom and Britain is sometimes used to mean the United Kingdom. Things are often perceived differently abroad, and even by some of the British themselves. The whole political entity is frequently referred to as England, even though England is only a part of it. That doesn’t usually bother the English, but it might bother the Welsh, the Scots and the Northern Irish. The best policy is to call the country the United Kingdom or, less formally, Britain. Call the people British, unless you know them to be English, Welsh, Scottish or Northern Irish or something else.

EDIT:

The title ‘The United Kingdom of Great Britain and Northern Ireland’ raises an interesting linguistic, as well as political, point. Syntactically, it’s ambiguous. Is it ‘(The United Kingdom) of (Great Britain and Northern Ireland’) or is it ‘(The United Kingdom of Great Britain) and (Northern Ireland)’?

In ‘The Isles: A History’, Norman Davies traces the various titles by which the isles have been known. From 1660 to 1707 it was ‘The Kingdom of England and Wales’. The union with Scotland in 1707 gave us ‘The united Kingdom of Great Britain’. Meanwhile, there was a Kingdom of Ireland from 1660 to 1800. In 1801, Ireland was included in ‘The United Kingdom of Great Britain and Ireland’. That state of affairs lasted until 1922 when Ireland divided, allowing the six northern Irish counties to become part of ‘The United Kingdom of Great Britain and Northern Ireland’.

The original ‘united kingdom’ of 1707 was so called because it united England (with Wales) and Scotland. The addition of ‘Ireland’ in 1801 and of ‘Northern Ireland’ in 1922 can therefore be seen as mere accretions to an already united kingdom. However, the grammatical ambiguity allows the alternative interpretation of all components of the State being united under a single crown. A good example, perhaps, of Engli-, sorry, British, compromise.

Solution 2:

English = of England
Great Britain = England + Scotland + Wales
British = of Great Britain (usually, but may also mean "of the United Kingdom")
United Kingdom = Great Britain + Northern Ireland

From the Wikipedia article Terminology of the British Isles, see images of the British Isles, the United Kingdom, Great Britain, and England respectively.

See the Euler diagram for completeness (the blue ones are legal entities, and green ones are geographical).