A lot of you here are leaning on dictionary definitions, which are entirely inadequate. If one or two bits of bread like elements with whatever filling in-between is all that’s required to satisfy the definition of sandwich, then why does no one ever classify eggs benedict as an ‘open-faced sandwich’?
I think that part of what is confusing the issue is that In north america (and possibly in the UK, I don’t know) that white fluff you guys call ‘bread’ is essentially the same as a burger bun. In EU, ‘bread’ means proper textured bread and burger buns are something else entirely. So to me, a burger is even farther off from a sandwich. Ingredients matter, as I explained with the eggs benedict example (and there are many others I could get into but skipping for conciseness).