Some differences are cultural, some differences are historical. How are Austrians that different from Germans? Flemish from Dutch? French from Walloons? Australians from New Zealanders? The historical context has created a certain divide between Canada and the US, which has resulted in differences in character and culture. But there are still strong similarities, of course.
Yet it really surprises me that after 6 pages, no one has mentioned the French-English duality. The coexistence (I use this term loosely) of two different cultures has shaped the country, and still does. Canadian politicians must speak French if they have national ambitions. About 20-25% of the population speaks and lives in French. One could argue that this says more about the difference between French Canadians and Americans, yet I believe that it has an impact on the country as a whole.
Canada is a wide country, and this duality is not clear everywhere. I was born and raised in Québec, and work in the Ottawa region. Here, you have a mix of English and French working together, in either language (...). It's quite interesting to see, and it definitely gives a specific flavour to the country. But it definitely is not the case in, say, Toronto or Calgary.
This country is indeed very difficult to define. For outsiders, both countries can indeed seem very similar. But saying that we are the same as the U.S. is, in my opinion, quite inaccurate.