Since you're looking at the WiFi only version I would guess there's no difference at all. Except that the cord will probably NOT come with a mains adapter whereas the UK version does, I believe, come with a UK 'plug'. But someone from the UK will probably be along soon and be able to verify that.

I think the difference is really only that, for whatever reason, you can only buy Kindle books from the UK site if you are in the UK. Which Ireland isn't.

But Amazon US can sell worldwide, subject to whatever international commerce agreements have been made.
Anyway, you shouldn't have any trouble connecting as long as you have or can get to a WiFi hotspot.