They are somewhat interchangeable, but if I bump into someone or I am trying to get by someone say in a grocery store, I say "unnskyld". If I hurt someone, like stepping on their toe, or I hurt their feelings, I will say "beklager". The safest thing is to use "unnskyld" in situations where you would normally say "excuse me" and "beklager" when you would normally say "sorry".
If beklager = sorry and unnskyld = excuse me, why is this sentence's correct translation shown as "No, sorry"? This kind of stuff really confuses me. Or, should the correct answer also show "No, excuse me"? Either could be right depending on the situation that caused someone to say this phrase...
I relate to your query, except I can't think of a time when someone would say, "No, excuse me", as a single combined reply. I can imagine being offered something and rejecting the offer and then wanting to get past and saying 'Excuse me' but as a separate, follow-up reply only.
I could see two people meeting up in a situation where neither was paying attention and one said "Excuse me" and the other says "No, excuse me." (they would likely put the emphasis on me because the situation was just as much their fault as the other person). Rare, but not out of realms of possibilities.
I don't know but it looks and sounds like the German word Unschuld which means innocence
Perhaps one would rather say unnskyld in a situation where he is innocent and beklager when he really has done something (like stepping on the toe).
I am just guessing but perhaps that helps to remember it...