I think this verb entschuldigen is very confusing and I cannot understand this verb entschuldigen (appologize in English).
Ich entschuldige mich., which can be abbreviated down to Entschuldigung.
Is a colloquial way of asking for forgiveness, as you understood correctly.
Ich bitte Sie um Entschuldigung.
Is the more proper and polite variant (because you ask to be forgiven, while Ich entschuldige mich. is telling the other, that you forgive yourself).
Entschuldigen Sie!
Can be used in three common situations:
Entschuldigen Sie! is used to interrupt someone, for example before asking someone for directions or help. You are asking for forgiveness for the interruption.Entschuldigen Sie! to get a crowd to part in front of you. Most people try to make way if they hear someone yelling Entschuldigen Sie! from behind.Entschuldigen Sie! can be used to ask someone to make excuses, most of the time because that person bumped into you accidentally. It is the polite variant of scolding someone, but is not that often used in modern times.A common variant is Entschuldigen Sie die Störung, where you ask the interruption to be forgiven.
This is most often used if you initiate contact with someone currently not responsible for customer service: You call the extension number of the head of department directly, or you knock at the door of a doctor/professor/official outside of office hours.
In that case you initiate with Entschuldigen Sie die Störung after they pick up the phone, or answer the door.
Entschuldigen Sie mich.
Is literally asking for forgiveness, but in that case you ask to be excused from attending a conversation / meeting / dinner.
If you need to go urgently (f.e. to the bathroom) you usually say Entschuldigen Sie mich. or more colloquially Ich muss mich kurz entschuldigen. and leave without waiting for a response.
Maybe that helps: In English, when a commanding officer tells an subordinate that he is free to leave he tells him "You are excused."
And as an extra, because it fits together with the last example:
If you tell an organiser that you can't attend a meeting she will note your name as entschuldigt in the attendance list.
Edit: Included comments by rdbury. Thank you!
In my opinion there is only one really polite formulation:
Frequently this is abbreviated to "Entschuldigung" which can be translated by "sorry".
However, many people use to say "Ich entschuldige mich". Although it expresses the same intention as "Ich bitte um Entschuldigung" and nobody will misunderstand this, it basically fails to say that you want to ask somebody to forgive you something that you have done (for example, having bumped him, having offended him with a thoughtless remark). Taking it literally, saying "Ich entschuldige mich" means I excuse myself. There is no real regret, in some sense you ignore the adressee and just say "oops".
