Éire, Cymru, Alba, Kernow, Breizh, and Ellan Vannin.

Ireland, Wales, Scotland, Cornwall, Brittany, and the Isle of Mann respectively.

They’re all related, but not the same. They all have different languages descended from a similar group, Irish (Gaeilge), Scottish (Gàidhlig), Manx (Gaelg), Welsh (Cymraeg), Cornish (Kernowek), and Breton (Brezhoneg). Some are more widely spoken than others, for example Welsh is still commonly spoken in Wales, whereas hearing Cornish in Cornwall instead of English is rare. 

All Celtic nations have varied mythology and culture.

Irish Mythology is different from Breton Mythology, and even Welsh and Cornish mythology (arguably the most related Celtic Nations) have subtle differences to each other. I wish I could add more about the cultures at this time but my knowledge of Celtic nations is primarily made up of the history and languages of those regions, particularly Cornwall. 

You might have notice that England and English are missing from this, because the English descended from Anglo-Saxons, who were German invaders that came to the isles right around the Fall of the Roman empire in the 5th Century, erasing the Celtic influence in what is now England. 

So what this all really means is that Celtic is an umbrella term, and just because it’s Celtic doesn’t mean it has anything to do with Ireland at all. So don’t assume that just because someone’s talking about something Celtic that they’re talking about something Irish.