I think OP is sorted but in summary for any one else and using my own situation as an example:
If you were born in Ireland you are automatically an Irish citizen. This is the category that my paternal grandparents fall into.
if you weren’t born in Ireland, but one of your parents was, you are automatically an Irish citizen. This bit confuses my dad, who falls into the category. He was born in London and has only ever had a UK passport and doesn’t think of himself as an Irish citizen, but he is. He could apply for a passport if he wished.
If you are the next generation down (me and my brother) then you ‘claim’ your Irish citizenship by going on the foreign births register. This involves supplying a shit load of original certificates - birth, marriage and death of my grandparents, birth and marriage certificates of my dad, as well his certified ID (as he is still living) and my own birth, marriage certificates and certified ID. Me and my brother are now on the FBR and are Irish citizens. We haven’t yet applied for a passport but we can do and I will do when my UK one is nearing expiration.
For my children and my nephew things get more complicated. My kids are a bit older and were born BEFORE I was entered into the FBR. They cannot be Irish citizens.
My nephew is younger and was born AFTER my brother was entered on the FBR . He can therefore also apply to be on the FBR and become an Irish citizen.
I am not sure if my nephew’s (hypothetical) children could also then go onto the FBR and be Irish citizens - I suspect not.