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> a sandwich includes at least two slices of bread

I guess open face sandwiches are not sandwiches.

As a Dane, I can confirm they are not.

Is a danish a kind of toast?

No, toast is a kind of Danish.

It is a kind of bread from Vienna.

To explain the joke, Danishes are called Wienerbrød in Denmark, aka Viennese Bread.

You can tell that just by looking at them.