of course canada shares a common history with the united states, but it's as reverse images of each other.
so, canada was initially a weakly populated french colony that was conquered by the british by accident. the british were colonizers in the true sense of the word, but the french were mostly interested in trading with the natives. so, the british created high density colonies and then expanded them, while the french scattered small trading communities at a day's travel distance from each other, from the mouth of the saint lawrence to the mouth of the mississippi - new orleans, st. louis, detroit, montreal...
when the british conquered canada in 1763 as a part of an unrelated conflict in europe, it was essentially handed over to the natives. it's not really clear if the british thought they'd seriously hold new france in the long run & the natives spent decades waiting for them to come back. but, for the purposes of our story, we have to point out that, in 1763, canada was almost void of british settlers - it was a french & indian colony, conquered in the french & indian war.
the first major movement of british citizens into canada actually happened between 1776 and 1793, as a consequence of the revolutionary war. so, while america fought a war for independence, canada inherited the loyalists - a shared history, but a mirror reflection.
the second major wave of immigration into canada came during the potato famine. given that the population of canada was very small at the time, this was a major event in our population history. in america, the irish were absorbed; in canada, they really changed the nature of the country. mirror reflections.
likewise, our constitution was written roughly contemporaneously to the american civil war, in the mid 1860s. confederation was 1867. and, we wrote our constitution to reject american governing traditions, because we fingered them as the cause of the civil war, which we didn't want. so, in canada, the division of powers is almost entirely reversed - and that's not an accident, it was done on purpose. the canadian framers believed that the cause of the american civil war was the constitutional protection of states' rights, and they made sure to keep it out of their own document because of it. mirror images.
and, i could continue, but i don't want to get too contentious by defining difference into the 20th century.
canadians don't broadly know the details, but we live the difference, intuitively. it's a true cultural, intergenerational memory in the sense that it's blurry in minutiae, but very real in broad scope.