I just thought I'd clarify my responses, cos I imagine that my take is different from others --- I'd guess that most of the people who have taken this poll are from North America somewhere (though I haven't checked) so I thought I'd drop in the opinion of someone from the UK.
That is: a sandwhich requires two slices from a loaf, with a filling in the middle. If you put a burger, or sausages or bacon, in between those slices of bread, then it's still a sandwich.
If there's only one slice of bread (even if that slice is folded back on itself) then it's generally 'a piece'. The filling for a piece is generally some kind of spread. For example, a slice of bread with jam on it is a 'jeely piece'.
How's that for a new perspective? :)
I'd guess that most of the people who have taken this poll are from North America somewhere