In Korean, what is the difference between 미안해 (mianhae) and 죄송합니다 (joisonghapnida)?
I was listening to Kpop and someone said 미안해 (mianhae) and it was translated to "sorry", but when I was online taking lessons, the teacher said that to say sorry you would say 죄송합니다 (joisonghapnida). What is the difference? Also, my romanisation might be a little wrong, I never actually learned how to properly romanise words.

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Glad to help.

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Thank you, Bryan! That really cleared things up. I'll remember that :D

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Quite simply yes the first one is like just a sorry the second one is like a deeper I'm sorry. When talking to my grandmother I will say mian meaning sorry, or mianhae meaning I'm sorry. When it's a minor thing I'm apologizing for like trying to say something and saying it wrong but when or if I ever do anything more seriously bad like eg. if I broke something I would say joesonghabnida the gist of it is like I have sin inside me. But for the most part I guess it's up to you.

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Thank you guys! I wouldn't mess with romanisation, but I get wor ried that someone won't be able to read the hangul and they will get annoyed with me. I don't know...and thank you, Jon for clearing that up. I think that 죄송합니다 is the more formal one. Is that correct?

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I agree with chin.billy.leung 100%! Use Romanization for at most the fist week as you learn Hangul. Then avoid it, drop it, skip it, ignore it at all costs. It is a crutch that will be very difficult to get rid of if you keep using it. Your ability to learn Korean and its complex grammar will be forever reduced.