Are the Ulster Scots/Scotch-Irish from Northern Ireland the same people/race as the Catholic Irish?

Yes, no, and all points in between.

No-one anywhere on Earth is 100% anything. Also, religion has absolutely nothing to do with ethnicity.

OK, Ireland. Ireland - north and south - has a complicated history. We're not really sure who the aborigines were, but (as with the aborigines of mainland Britain) they were subsumed into the Celtic nations (note the plural - the Celts themselves were a diverse lot) around 1200 BC (give or take a couple of centuries).

Ireland - Hibernia as it was then - was never settled by the Romans, which remains the biggest cause of ethnic and cultural difference between Ireland (as a whole) and Britain. Not only because of the direct influence of Rome, but because legionaries in Britain were drawn from all over the Empire - men from Syria and Thrace and Mauretania all served in Britannia and (human nature being what it is) formed relationships with local women.

Fast forward to the ninth century. Ireland is still basically a Celtic land, but there is no Kingdom of Ireland. Yes, there was a High King from time to time, but he was more of il capo de tutti capi - with some (but not much) influence over the Kings of Ulster, Munster, Leinster, Connaught, Meath etc.

At this time the Norse (Vikings, if you like) arrive. Mainly from Norway, but some from Denmark. One things the Norse do is to found the City of Dublin. Following their usual practice (practice, not policy) the Norse settle, interact and intermarry with the locals, and soon become more Irish than the Irish - in the same way that their cousins who founded Normandy soon became effectively French.

Already, we have a lot of ethnic mixing, both north and south. Then in the twelfth century, we get the Normans. The Normans are Norse who settled in France and subsumed French culture (and genes), then who settled in England and subsumed English culture (and genes), then moved on to Wales... then finally to Ireland. More racial and cultural mixing.

Another fast forward to the time of the Reformation. By this time each King of England styled himself King of Ireland (and France, usually) though this was mostly wishful thinking. There was an English presence in Ireland, centred round Dublin (known as the English Pale), but the influence of English Kings over the rest of Ireland waxed and waned through the centuries.

The Reformation threw a large spanner in the works. Religion has caused more trouble than anything else in human history, and it's high time it was stamped out, but that's another topic. The pint is that whilst England and Scotland (mostly) converted to Protestantism, Ireland remained stubbornly Catholic. This was intolerable, so some bright spark came up with the idea of settling English and Scottish Protestants in Ireland, to show them the error of their ways. This process - known as the Plantation of Ireland - had mixed success.

The most successful "colonies" came in the north, mainly because a power vacuum developed there from 1607 (look up the Flight of the Earls, if you're interested). Scots presbyterians settled in Ulster, and a contingent of Londoners settled in Derry. This is why Protestant Irish emigrants to the US are called Scots-Irish (they're called that in America, but nowhere else on Earth), and why the city of Derry may or may not have changed its name to Londonderry (even today, it depends who you ask).

In the four centuries since then, there has been an awful lot of social mobility - both in Ireland (people from the North moving to the South and vice versa), and between Britain and Ireland.

In other words, the collective DNA of the various people of Britain and Ireland has been so mixed over the centuries that the idea that there's a separate ethnicity between Northern Ireland and the Republic is nonsense. Separate political philosophies yes; separate ethnicities no.  

 Scots/Scotch-Irish came over on s giant pick up truck with a rebel flag

What the first anon said.  Ethnos is cultural.  Get a map out and have a look at it.  Bonus if it's a good topographical.

The region that is Ulster has easier connections with the west coast of Scotland than to the south over the mountains of Mourne.  In the ancient world water unites, land often divides.  The Scoti after whom Scotland is named originated from Ireland, more to the point, Ulster.  Conversely there were Picts, another constituant Scottish people, in Ulster.  The much later Ulster Planters came from the Scottish Borders and originated from a mix of Scotland's ethnicities, including Angles and doubtless some leftover Britons - but by that time they just thought of themselves as Scottish.  After Plantation it's not like people didn't mix either, but it's like with racism, mixed people are made to pick a "cultural side" and disavow the other.  It's interesting what you find if you start to dig in historical sources.

The point is, people have been travelling back and forth between Ulster and Scotland and mixing for literally millennia.  It's a cultural continuum.  The Reformation is a blip on that timeline, even though it's created hundreds of years of unrest.

Until recently an Ulster Scot who was Catholic wouldn't be tolerated by their social network.  They'd be coverted into "soupers" and by the next generation they'd be fully fledged Papists with an odd predilication for traybakes over scones.  You do realise that this is all wrapped up in politics?  You haven't met insane until you experience having the contents of your shopping trolley scrutinised by every nosey busybody for signs of protestantism or catholicism if you're an unknown personage because everybody would look the same except for tiny cultural hints that they belong to one camp or the other.  It's got bugger-all to do with DNA.

"American" is a nationality, not an ethnicity.

Religion has no impact on ethnicity or DNA.

DNA shows genetic connections, not distinct regional connections except in a very general way across centuries.

You're looking at genealogy the wrong way. If you want to find your roots, you must follow a paper trail.