Citizens of the United Kingdom are British, which is where the confusion starts as "Britain" while commonly used and understood doesn't really refer to a geographic area though is often used interchangeably for "United Kingdom".
While citizens of all of the component parts of the United Kingdom may be referred to as British, you should be aware of is that "British" is NOT the same as "English". Referring to one of the 16% who is British but not from England as "English" will probably result in a correction on a scale of a jokey "It's ok, but.." - to terse and tight lipped.
Political - United Kingdom + Republic of Ireland
Nationalities - British or Irish
Population 2016: 70.3 million
- United Kingdom
(The United Kingdom of Great Britain and
Political - United Kingdom
Nationality - British (those born in Northern Ireland also have automatic Irish citizenry)
Population 2016: 65.6 million
- Great Britain
Political - n/a
Nationality - British
Great Britain is the name of the largest island, it contains most of England, Scotland and Wales apart from the smaller islands.
Political - England
Nationality - British and English
Population 2016: 55.3 million
Political - Scotland
Nationality - British and Scottish
Population 2016: 5.4 million
Political - Wales
Nationality - British and Welsh
Population 2016: 3.1 million
Political - Republic of Ireland and Northern Ireland
Nationalities - Irish or British
Population 2016: 6.5 million
Political - Republic of Ireland (Eire)
Nationality - Irish
Population 2016: 4.7 million
Political - Northern Ireland
Nationality - British and Irish
Population 2016: 1.8 million
Got that? Don't worry, many British people would have some difficulty in explaining it all too, just don't go calling everyone English when they might not be, even if they are British.
Strictly speaking the citizens of the UK are British and not English, Scottish, Welsh or Northern Irish, there is however no consensus as to how the terms should be applied and so everyone essentially has a catch-all nationality of British and then a more specific one as well.
The Republic of Ireland is part of the British Isles but is not part of the United Kingdom or Britain.
There is often confusion at many levels, for instance our team in the Olympics and some other sporting events is called "Team GB" for Great Britain when that is just the name of the largest island, "Team UK" would be more accurate, but GB it is.
I get a regular reminder when filling in any online form that asks for my nationality with a huge drop down list and have 3 different places to look for a choice when there's only any one of the 3 there, England, Great Britain or United Kingdom.