If we look at the American revolution, one of its causes was Britian's restriction on expansion. Hence through manifest destiny, the United States got so big. So how did Canada get so big (coast to coast), despite being a colony for much longer and therefore forced to abide by the same restrictions?
The first poster is correct in part. In the wake of American expansion to the west there was greater urgency to match it. Also attitudes towards indigenous people "evolved" significantly in the same time period.
British notions continued to assert themselves compared to the United States. Treaty-making became critical to Euro-Canadian expansion into the west. Treaties, generally, preceded colonization.
This is not in order to excuse the genocide and expulsions that occurred. The treaties created a legal framework for Canada to annex the next chunk of the continent.
The vision to unite Canada from sea to sea to sea came later. It was originally governed as British North America, the hodge podge of colonies Britain had left after the American Revolution. After Canadian confederation prominent leaders set about uniting all British territories in order to fed off the Americans and create prosperity.
This is pretty simple, but covers the gist.