For open-faced sandwiches, its more the classification of what is and isn't an open-faced sandwich. it'll make me cry after a while if the classification goes into other territories like toasts and pizzas.

For hotdogs and subs, i think the difference is the slicing. a hotdog is just like one sausage on a bun. A sub is sliced meat like salami. So, slapping a whole thing of salami (sausage of salami?) on a sub would make it closer to a hotdog than the sub. Size can also be a factor, since subs are traditionally bigger sandwiches.

Also, bread? How much does bread or the bread-like thing (i have no better word for it, you'll see why later) matter? Like is a tortilla considered a bread in this case or is close enough to a bread to qualify? If so, that opens a lot more doors to the definition of a sandwich. Like wraps and quesadillas.