You're confusing two different groups of 'Irish'. Appalachia is associated with the Scots-Irish, a term used mainly in America to describe a group of people from northern England/southern Scotland (the Borderlands) and what is now Northern Ireland, predominantly Presbyterian and/or non-Anglican Protestant in religion. They emigrated in the mid-1700s. Andrew Jackson is a good example. His family were from northern England, and migrated to northern Ireland, staying there for a generation only and then moving to the US.

Irish Catholics are a different ethnic group, and they did not begin to emigrate to the US in large numbers till much later (1840s onwards), settling mostly in Northern cities. JFK is a good example.

Edit: I want to add a source, especially for American readers: David Hackett Fischer's "Albion's Seed: Four British Folkways in America". It goes into great detail about the characteristics of this group (religion, settlement patterns, political mores, etc). That book really is a top 5 for American history buffs. And while I'm here, DHF's "Historians' Fallacies: Towards a Logic of Historical Thought" is great for learning about how to think about history. Both were vital for me in understanding America in particular and the subject of history in general, and I hope ye gain from them.