It's undeniable. Ireland was part of the UK for a long time and many things remained essentially the same after independence. To this day the countries have incredibly close links especially commercially but also culturally.

The main difference between the scenarios is that in spite of the closeness between Ireland and the UK there's significant and, among a minority, even militant antipathy on the Irish side toward Britain whereas I believe Canadian-American relations are almost entirely cordial (the occasional snark aside).