Detroit is in the SE part of Michigan, on the Detroit River which connects Lakes Erie and St Clair. Just across the river is Windsor, Ontario ... just the width of the river away (a couple of miles.) Detroit is right on the Canadian Border at that point.
The Detroit River is technically a "strait," a narrow passge between two larger bodies of water. (In this case, Lakes Huron and Erie.) A river is defined as a stream that drains water from higher elevations into a large body of water.
No Detroit is closer to the canada-usa border because Detroit's downtown is right on the waterfront of the Detroit River and downtown Buffalo is afew kilometers east of the niagara river and the border slants away from the city at lake Erie.