I have been able to identify two aspects where the English language distinguishes between shame and embarrassment:
Shame relates to having done something wrong, while embarrassment is a result of having done something foolish.
One can be ashamed of oneself without anyone else knowing about it, but embarrassment is usually something you experience in the eyes of others.
I wonder how these nuances are handled in German? In addition to this general question, I also have a more specific question along these lines. I recently tried to translate the phrase “she all but died of embarrassment” in the context of someone who peed her pants while laughing at a joke. I have been given at least three choices for “embarrassment”, which I will perhaps withhold until I see what other people would like to offer.
(The question originally arose in the Yiddish context, where we have in addition to the three German options I know of, at least three Hebrew terms to choose from. I still don’t know which one exactly hits the mark for the case of peeing your pants.)