'미안해요' (mi-an-hea-yo) mean "I'm sorry".
However '죄송합니다' (jwi-song-ham-ni-da) to my knowledge is more honorific form of "I'm sorry" but can also means "Excuse me" or "Pardon me".
If you are talking to a friend or someone younger than you say '미안해요'. To someone older or in a high position '죄송합니다'.