oooooh boy. Might want to do some research before your holiday to Belfast (or Derry).
Edit -
I realize that came off snarky - it was meant lightheartedly. In all seriousness, though -
Republic of Ireland - a soverign nation of 26 counties. Split from the UK nearly a century ago. There's some interesting (but very painful) history behind that.
Northern Ireland - 6 counties at the northeast of the island
Ireland - a geographical entity (the island itself)
Ireland (or Eire) - the official name of the Republic
Great Britain - the island with England, Scotland, and Wales. Often used to refer to the UK (but this isn't completely accurate, if we're being pedantic it's a geographical, not political, term, and there's still Northern Ireland).
United Kingdom - England, Scotland (for now), Wales, and Northern Ireland
It would make sense for me to make an error in there, but I think I've got that right. Hope it's helpful!