Correct, you do not need to change trains on the Maple Leaf when riding from NY to Toronto. The entire train, including the engine runs through to Toronto. Of course they still change the engine in Albany, but no change at the Canadian border. Canadian customs will board the train in Niagara Falls, Ontario and clear everyone without leaving their seats, assuming that all their paperwork is in order.

The Amtrak crews gets off the train in Niagara Falls, ON and VIA rail crews take over at that point. And by crews I mean both the operating crew (engineer & conductors) as well as the on board service crew (namely the cafe attendant. In fact VIA boards its own food at this point, giving one an opportunity to buy something that one normally can't ever get on an Amtrak train, that being Coca-Cola. Amtrak is a Pepsi product user, unless a State pays for the service, in which case they can set the menu.

So to the OP, that $1 for a BC seat buys you the rather nice faux-leather seat with foot rest and calf rest that one finds in the Club-Dinette car. This car also offers the 2 & 1 seating, so the seats are much nicer and roomier than normal coach seating. The cafe is the other half of the car, so the walk is real short.