Where I grew up the various terms had very specific meanings...
A sandwich was just that, something between two slices of bread. A hot roast beef sandwich would be, literally, hot roast beef on a top and bottom bun; same with a cold roast beef sandwich.
Open faced sandwich wasn't used as commonly, but was still out there. Most tuna melts are open face sandwiches.
But, in central Pennsylvania, if you saw open-faced hot turkey sandwich (or roast beef, or meatloaf, or hamloaf, etc.), you KNEW you were getting a base of bread, hot turkey, hot gravy over that, and mashed potatoes. Depending on the restaurant you might get the spuds on top of the turkey with the gravy done volcano style, or you might get the spuds on the side of the plate, or even in a separate bowl.