The exact wording of the Buckingham Palace press release:
The Queen has been pleased to accept an invitation from the President of Ireland to pay a State Visit to Ireland this year. The Queen will be accompanied by The Duke of Edinburgh.
Given the natural sensitivity of people over the distinction, my first thought was that the palace and BBC should probably have drawn a more clear distinction and referred to Ireland as "The Republic of Ireland". But then I popped over to the official Irish Government website of the President, and I see that THEY also refer to the lady and her office as the President of Ireland (not President of the Republic of Ireland). Elsewhere on that website (and other Irish government websites), it refers to the country alternately as "Ireland" or "The Irish State", and only uses "Republic of Ireland" in the most formal of language.
So clearly in diplomatic usage, "Ireland" - without qualification - is accepted by all parties to refer to the Republic of Ireland, whilst "Northern Ireland" refers to the British territory. BP and BBC appear to be merely following suit.