Let's put aside, for a moment, the fact that Canada is a country with two languages and therefore two solitudes.
Even just isolating English Canada, it is difficult to pin down a pan-Anglo Canadian identity due to the fact that we are a long, thin 6,500km wide country where all of the population is clustered within a few hours' drive of the US. Effectively Chile turned on its side, with the world's cultural hegemon at our doorstep!
But I'd say that defining ourselves as "Not American" is fundamental to our identity, whether in BC or Ontario or Nova Scotia, beginning with the post-Revolutionary War migrations to various provinces that Acajack brought up.
At first this sounds petty, but it is the way a lot of cultures define themselves. There's a term for it too -
schismogenesis: the practice of defining oneself as radically different from one's nearest neighbour.
While Canadians speak the same dialect of English and have the same cars and homes* and food** as Americans, they have a very different set of values, and approach to life and general day-to-day life is quite a bit different than outward appearances would suggest. While Canadians can obviously blend more fluidly into American life than people of any other nationality, there's a deeper layer to America that Canadians don't really penetrate and can't really understand until they live there. You see the same in reverse: Americans who moved to Canada as adults and have moved here permanently toggle their attitude between "going native", and being America's harshest and loudest critics, and feeling homesick and complaining about how lousy things are in Canada. While they can speak the same language and expect the same consumer goods, they still approach life in Canada as a foreign country, no different than if they moved to a non-English speaking country in Europe.
* Canadian and American homes and their layouts/furnishings/size are diverging again. They probably came closest to overlapping in the late 1990s/early 2000s. So much more of our population lives in housing types like highrise condominiums and stacked townhomes, and the types of furniture that fit into these spaces is very different. You can see huge differences in Canadian attitudes to home furnishing when you consider that every Canadian city above 500,000 has at least a small format IKEA, often a full-sized store. There are American metros like Cleveland with 4+ million people within an hour's drive that have none.
** Canadian food has diverged considerably from American food due to each country's immigration patterns and the rise of the US South. American food is mostly Tex-Mex and Southern these days. Again, before the 1970s, I think standard American and English Canadian food were much closer. If you're a white Vancouverite under 45, you probably know what Xiao Long Baos are. If you're a Torontonian you've had a beef patty or Roti.