Hmmm.. So we have 3 sentences to say I AM SORRY in Swedish language which depend of sitation. 1) URSÄKTA - that is more like EXCUSE ME - for example if we want to ask some one for something on the street. 2) FÖRLÅT MIG - I AM SORRY, when we made something wrong 3) JAG ÄR LEDSEN - I AM SORRY, when someone will tell something sad (for example that something died). Something like polish PRZYKRO MI.
Am I wrong?
From what I understand, the "led" in "ledsen" is related to the "leid" (pain, discomfort) in "tut mir leid" in German. Which can mean "I'm sorry" but literally means "It makes me hurt/it pains me". So, “ledsen” kind of means “feeling bad emotionally”, which pretty much covers sadness and regret.
In English it is very different and confusing. The concept of “sorry” and “sad” are still close cousins, but contrarily to Swedish, English created a term specifically for sadness and reserved “sorry” for “feeling regret”. But “sorrow”, although more closely etymologically related to “sorry”, is closer in meaning to “sadness”. In old English, “sorrowful” is “sorgful”, similar to modern Swedish “sorgsen”.