This always seems very strange to me in terms of our cultural geography. It's fairly popular to class Ireland together with Wales, Scotland, Brittany, Cornwall and the Isle of Man under the Celtic heading. But I would say out of all these we only really feel a strong affinity to the Scots. We share similar historic languages, we have similar cultural traits, there's been lots of movement back and forth over the centuries between us. It's still not particularly close (in the way that, say, the Scandinavian countries all feel bound together), but we recognise ourselves in each other to some degree.
For the rest, the connections seem to be more academic (languages, legends and mythology) than anything really tangible in the modern day. I think it's particularly surprising with Wales - they're right across the sea from us, stuck in between ourselves and our historical overlords (who definitely loom large in our minds). Historically speaking any route from our east coast which didn't travel directly north had to skirt past Wales at some stage. It's still a big part of the modern overland route to England, whether through Holyhead or Fishguard or anywhere else.
But Wales really doesn't feature in our cultural worldview. Our languages diverged thousands of years ago and they are very different nowadays, on the surface it's quite hard to see any connections between them. There wasn't a movement of people between us in the same way that there was across the Straits of Moyle to Scotland, even in modern times very few Irish people seemed to have settled in Wales specifically. Politically we've never been close either, as far as I can tell. And even to the average Irish person, we would tend to know very little about Wales other than experiences from taking the ferry or the annual Six Nations clash. How many Irish people would know about the Eisteddfod? Or who Plaid Cymru are?
Geographically speaking, they are the nearest neighbour for most of us. So why aren't there deeper ties between us? Did British rule stifle the connection maybe? Are they too small to exert much influence on us? Or is there actually a real connection that's just a bit less obvious.