Just to clear this up for anyone interested:
'Great Britain' is just England, Scotland and Wales. 'The United Kingdom' is made up of Northern Ireland, Scotland, Wales and England. 'The British Isles' is the geographical definition of Great Britain, Northern Ireland and the Republic of Ireland. This is why on British (anybody from the United Kingdom) passports it says "The United Kingdom of Great Britain and Northern Ireland" :)
Just to add more confusion, you may be thinking that "British people" by that definition are those from Great Britain. But quite often Northern Irish people declare themselves British, as they are ruled by the British monarch. But depending on their political stance, they may declare themselves Irish.