Ireland (or the Republic of Ireland, Poblacht na hÉireann) is a sovereign, independent country occupying five-sixths of the island of Ireland in the North Atlantic.
The remaining one-sixth of the island is Northern Ireland, part of the United Kingdom. The 1998 Good Friday Agreement governs cross-border relations.
So: "Ireland" = the Republic (country). "Northern Ireland" = UK region. The island = both.