Nitpick: There aren’t any “Northern Ireland citizens”; people from Northern Ireland are citizens of the United Kingdom.
But your basic point is correct. Anyone born anywhere on the island of Ireland before 2005 is an Irish citizen by birth. Their children, if born if born outside Ireland, are Irish citizens by descent. (If born in Ireland, they are of course themselves Irish citizens by birth.) The grandchild of an Irish citizen by birth wasn’t automatically an Irish citizen, but was entitled to become one, which they could do simply by registering
Since 2005, people born in Northern Ireland are not automatically Irish citizens, but they are entitled to become Irish citizens, which they can do either by registering or simply by exercising any of the incidents of Irish citizenship - applying for a passport, voting in an election where the franchise is confined to citizens, etc.