Maybe that's about personal preference or sprachgefühl, but for me, there's a huge difference between Sandwich and Butterbrot. A Butterbrot is really just that, bread and butter. Käsebrot is bread and cheese and butter. A Sandwich is more, it is stuffed with vegetables, maybe cheese or different sauces and might as well be toast or baguette. 'belegtes Brot' fits that much better than Butterbrot. My favourite Sandwich contains ketchup, salad, falafel, tomato, pickles and mayonnaise, stuffed between two slices of toast, for example. I would never call that 'belegtes Brot', for me, that's a sandwich. Duden saysthe following about 'sandwich': »zwei zusammengeklappte belegte Brotscheiben«.
For me "belegtes Brot" is an open faced sandwich. I would never use the word "Käsebrot" unless the cheese is baked right in with the bread, ie. Cheese bread. We would say "Butterbrot mit Käse, Wurst "etc. When I speak to Germans in Canada, we use "Sandwich" for English sandwiches, such as you describe, using soft, spongy white bread. Anything on rye would be a Butterbrot regardless of what goes with it. But I see now that Germans don't seem to make that distinction. I also saw that in Wiktionary the German "Sandwich" has 3 plurals 1.Sandwichs, 2.Sandwiches, 3Sandwiche. With such confusion I'll stick to Butterbrot thank you very much:)