That really doesn't capture the flavor of it. In a very real sense, the first Americans were British -- they just refused to pay taxes to a government thousand of miles away.
The US never tried to take over the territory later called Canada, whether to annex it or to remove the British. There was never a war declared for that purpose, the US never mobilized its full military toward that aim, there was never a large amount of financing raised to pay for such an immense effort, and so on. There's zero evidence to support the notion that US planned to try to accomplish that outcome. At best it was a skirmish toward a narrow goal.
That really doesn't capture the flavor of it. In a very real sense, the first Americans were British -- they just refused to pay taxes to a government thousand of miles away.