Glad to help.

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

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.

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?

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.