1. 습니다/ㅂ니다
it is Hasipsio-che(하십시오체)* ending suffix
This conversational style is generally called either the "formal" or the "formal polite. 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 colleagues in more formal settings
by TV announcers
to customers
Both 습니다 are ㅂ니다 are same patten with different form.
습니다 is used after verb/adjective which ends with final cosonant.
ㅂ니다 is used after verb/adjective which ends with vowel.
e.g.
먹다 -> 먹습니다.
찾다 -> 찾습니다.
가다 -> 갑니다.
오다 -> 옵니다.
2. 십니다
it is combination pattern of 시 and ㅂ니다
시 is a suffix which denotes the subject is elder person than the speaker.
으십니다 is used after verb/adjective which ends with final cosonant.
십니다 is used after verb/adjective which ends with vowel.
e.g.
먹다 -> 먹으십니다.
찾다 -> 찾으십니다.
가다 -> 가십니다.
오다 -> 오십니다.
* usage examples
나는 학교에 갑니다.(The subject is same or younger than the speaker and the listener is elder than the speaker)
아버지는 회사에 가십니다.(The subject is elder than the speaker and the listener is elder than the speaker)
나는 학교에 간다.(The subject is same or younger than the speaker and the listener is younger than the speaker)
아버지는 회사에 가신다.(The subject is elder than the speaker and the listener is younger than the speaker)