Do the British include people from Northern Ireland?

No. It's part of the UK. There's a long history to it as to why it's not considered part of Ireland, but if you want I can tell you a brief bit.

The UK wanted all 32 counties of Ireland, and for a while they had it. But the Irish people wanted full independence. There was a long war, gruesome. It was horrible and it had guerilla tactics. Michael Collins, who was leading the IRB (Irish Republican Brotherhood, now it's IRA) was sent over to England by Eamon De Valera (President of Ireland at the time). They signed a treaty that meant we have full control of Ireland, except for the 6 counties of Northern Ireland. We now have the Republic of Ireland, which has 26 counties which are fully 100% Irish.

The people of Northern Ireland are citizens of the United Kingdom of Great Britain and Northern Ireland, so yes, they are British.

It all depends on why you're using the term. Culturally, the term "Brits" usually encompasses citizens of the United Kingdom (England, Scotland, Wales, and Northern Ireland). But in terms of, say, civil rights, one might include the inhabitants of the UK and all of its overseas possessions e.g. the Channel Islands and the Falkland Islands.

Hope I helped!

british - english, welsh, scottish and irish. ireland for irish = northern ireland and eire. northern ireland is united kingdom but not great britain. but looking at the other answers, we can't all be right.