입니다 comes from 이다. (is, are) 있습니다 comes from 있다. (There is, There are) This is a tree. 이것은 나무다. 이것은 나무입니다. -more polite There is a tree. 나무가 있다. 나무가 있습니다. -more polite

Hello Angel! 입니다 = This is the formal standard tense form for the state of being verb 이다. We often use this verb when introducing ourselves to strangers in Korean. EX: 제 이름은 Garrett 입니다. 있습니다 = This is the formal form of the existence/possession verb 있다 which you can use to say something exists or someone owns/has something. EX: "차가 있습니다," means "I have a car." Remember that the ㅂ니다/습니다 ending is a very formal ending that is only used in specific cases with certain relationships and people. The 요 form is the most common polite form in daily conversation form most sentences, but, again, it depends on who you are talking to and your relationship with them. Hope that helps!