Hi Cindy,
I have been basing place names on possession. It is a fact that the population of Detroit during the 1783-1796 period would have identified as British and there was a British garrison present. When the US took possession there was a large evacuation of people who wished to remain British subjects. They settled on the south shore of the Detroit River, establishing the town of Sandwich at that time. (Now part of Windsor, Ontario)
The Canadian side of the river was part of Upper Canada after 1791. As for the War of 1812, the British forces only held Detroit for thirteen months, from August 1812 until Harrison recaptured it for the Americans in September 1813. That fall, the Americans took possession of Sandwich and much of the southwest of Upper Canada and held it until the end of the war. But in this case, the residents of Michigan and Upper Canada would have identified as such. During the war, the only British in Detroit or Americans in Upper Canada would have been occupying soldiers.