I'm sorry & excuse me: 죄송합니다 / 저기요

• Polite (존댓말) I'm sorry

죄송합니다
Meaning: I'm sorry.
Unlike "I'm sorry" in English, it is not suitable for feeling bad for someone's misfortune. It is only used for apologies.
"죄송하다" is the base form verb. 죄송하다 does not have a casual form.

• Casual (반말) I'm sorry

미안해
Meaning: I'm sorry.
Just like "죄송합니다", this means only apologies.
"미안하다" is the base form verb. "미안합니다" or "미안해요" also can be used as a polite form. "합니다" and "해요" are almost always exchangeable, except "합니다" is more formal than "해요".

• Excuse me

저기요

Meaning: Excuse me.

Unlike "Excuse me" in English, "저기요" is only used to get an attention from others, e.g. to get an attention from a stranger who dropped a wallet to notify, or to get an attention from a waiter at a restaurant. It is not suitable for excusing yourself.

Quizlet: https://quizlet.com/_1vw06r