미안합니다. 죄송합니다. These are just two ways that Korean people say "I'm sorry." But these two phrases don't work in every situation. In some cases, you'll want to use the verbs 안타깝다 or 안됐다, or the phrases 어떡해요 and 유감입니다. Each one is a little different in meaning, and also has a different use.
Find out their differences, and when to use them, in this first episode of the new series "A Glass with Billy."