The size and significance of the Irish presence in Canada is widely underestimated. We are the invisible ethnicity.
Nicholas Flood Davin gives the math for 1877: Ontario then held 559,440 Irish, 328,889 Scottish, and 439,429 English. Canada at Confederation contained 846,414 Irish, 706, 369 English, and 549.946 Scottish—the Irish numbers second only to the French. In the West of Montreal, “les Anglais” of the day were in fact 19,394 Irish, 7,974 Scottish, and only 9,099 English. So, if we are indeed going to speak of “two founding nations” in Canada, those two are: French and Irish.
But even that is not the whole story. Estimates are that the “French” population of Quebec, through intermarriage, is up to one quarter Irish by blood. Marguerite d'Youville's stepfather was Irish. Loius Riel's ancestor changed his name to Riel from Reilly. Louis Saint Laurent's mother was Irish; so was George Vanier's.
I submit that this has left a massive stamp on the Canadian culture and character. There is a real mainstream Canadian culture, and it is essentially Irish.
Irish-Canadian culture is also different from Irish-American culture, or Irish-Australian culture, for several reasons. Notably, the Irish of Canada came mostly from Ulster, and were primarily Protestant. Those in America and Australia came mostly from the south and west, and were primarily Catholic.
Unlike the US, the Irish were also already well established in Canada before the Great Famine. However, even at the time of the famine, there were more Irish emigrants to Canada than to the USA, and those who landed in Canada tended to be the poorest and most destitute. The passage to Canada was significantly cheaper—because there were fewer safety and health regulations in Canada, and because the lumber trade meant many ships were otherwise empty on their westward journey.