There are seven verb paradigms or speech levels in Korean, and each level has its own unique set of verb endings which are used to indicate the level of formality of a situation. Hasoseo-che (하소서체) Formality very high Politeness high archaic ex) 미안하나이다 Hapsyo-che (하십시오체) Formality high Politeness high ex)미안합니다. Haeyo-che(해요체) Formality low Politeness high ex) 미안해요. Hao-che(하오체) Formality high Politeness neutral Currency uncommon ex) 미안하오. Hage-che(하게체) Formality neutral Politeness neutral older generation ex) 미안하네 Haera-che(해라체) Formality high Politeness low ex) 미안하다 Hae-che(해체) Formality low Politeness low ex) 미안해 Refer to https://en.wikipedia.org/wiki/Korean_speech_levels 1. 미안합니다 is Hasipsio-che This conversational style is generally called either the "formal" or the "formal polite." This is a common style of speaking. A conversation with a stranger will generally start out in this style and gradually fade into more and more frequent haeyo-che. It is used between strangers at the start of a conversation among male co-workers by TV announcers to customers 2. 미안해요 is Haeyo-che This speech style is called the "polite" style in English. It is remarkable in that it is used both with higher level pronouns. It is used mainly: In Korean phrasebooks for foreigners. Between strangers, especially those older or of equal age. Between female co-workers or friends. By younger speakers as a less old-fashioned alternative to the hao-che. By men and women in Seoul as a less formal alternative to the hasipsio-che. 3. 미안해 is Hae-che This conversational style is called the "intimate" in English. It is a defective paradigm, meaning it lacks most of the expected conjugational forms. It is used Between close friends and relatives. When talking to children. You can use Hasipsio-che for anyone older than you. You can use Haeyo-che for younger strangers/anyone not intimate same age with you. You can use Hae-che for children/intimate friends/family

I'm really interested in this, too! Maybe Tony can help us, he has helped me a bunch twice with my simple Korean questions :)