Burger (Hรคhnchen (chicken) burger)
This is what you would find if you google it in German. So it's the commonly understood use of the words.
(also, if you want to get really specific, a sandwich is a certain type of bread and if the sandwich is made with other types of bread, then it's a belegtes Brot/Schnitte/Bemme/Stulle. But you can use sandwich for both, so I'll let it pass.)
Edit: I feel like it's important to remember that while "burger" is an English word, it's a loanword for us in Germany. So it's part of our language and therefor has a specific meaning and that meaning seems to be different from the original English one. Lots of examples of this exist. We don't use the word wrong, we speak a different language that happens to share this word.
2nd Edit (sorry not sorry): You can refer to the Brรถtchen in the second image as a sandwich. I think Brรถtchen is more correct but it's sold as a sandwich in some bakeries and people know what you mean. If it's a baguette then things get really interesting because I feel like with a baguette, sandwich is more accurate than Brรถtchen even though based on the properties of the bread, it should be a Brรถtchen.
None of this matters, the TL:DR stays the same, which is that we define these things by the bread and not what's between the bread.
3rd edit: If all or most English-speaking countries agreed on one definition, then I think you would have the right to correct our use of the word burger when we use it in English. But if, for example, the meaning varied between the US, the UK and South Africa, then I'm sorry, US-Americans, but you don't get to dictate language.