I am not sure how many times I have to explain this, but let's see if this one finally gets through.
The Irish Rebellion occurred in 1641, ending in 1642 with the Irish winning the war and setting up an Irish government to control Irish affairs. This was called Confederate Ireland. They won their rebellion. Cromwell, who arrived in Ireland in 1649, cannot be putting down a rebellion that ended 7 years before his arrival. He was making an attempt to reconquer Ireland after Great Britain had lost control of it to the Irish. How is trying to reconquer one place years after a rebellion ended different from trying to reconquer another place? Remember....Cromwell arrived 7 years after the rebellion ended.
This isn't right. The wars in Ireland continued long after 1642, and the Confederates never controlled the whole country. They weren't fighting with Great Britain at the time, either, since there was no such beast. James I did use the term informally to refer to the personal union of the kingdoms of Scotland and England under himself, but that union had been torn asunder by the civil wars.
The Confederates were fighting variously against English and Irish Royalists, Parliamentarians, Scottish covenanters who invaded Ulster in 1643, and Irish nobles who feared the loss of their power. They eventually tried to form an alliance with the Royalists, some of whom were Protestant, against the Parliamentary forces, leading to many of the Confederate leaders being excommunicated by the papal nuncio, who had brought money from abroad to try and establish a papal state. This was all before Cromwell's arrival.
To clearly see that Great Britain didn't exist at the time, we just have to look where Cromwell invaded after Ireland - Scotland, where the hardcore Protestant Covenanters had declared Charles II king in exchange for his agreement to impose their strict, anti-episcopalian brand of Protestantism on England and Ireland, as well as Scotland. This was somewhat ironic, as it was the Covenanters who had been the first to take up arms against the crown in 1638. Charles was almost certainly lying for political gain, as he had some sympathy for Catholicism, and supposedly promised to convert some years later to get military support from the King of France.
The main thing I'm getting at here is that anyone who tries to present the complex wars and revolutions of Britain and Ireland in the seventeenth century as some kind of simple 'Catholics vs. Protestants' struggle either doesn't know much about them, or is intentionally misrepresenting them for religious or nationalist motives.