이다 and 있다 are two different verbs that together correspond to the function of "be" in English. 1. 이다: like "is" in "AA is BB" (AA는 BB이다). It equates AA with BB. 2. 있다: like "is" in "There is AA" (AA가 있다). It means AA exists. 이다 is a special verb (technically a "particle") which directly attaches to a noun with no space. - 나는 학생이다: I am a student. - 지는 것이 이기는 것이다: To lose is to win. 있다 is more like other verbs in its usage. - 책상 위에 책이 있다: There is a book on the desk. - 문제는 우리의 내부에 있다: The problem is/lies within us.

In short, 이다 is used to equate one thing to another (like an equal sign). 있다 is used to show existence. These are two very different things. Saying "There's a mouse in my room" ("There is" shows existence) is much different than saying "My room is a mouse". They are two very different verbs. "I have a cat" ("have" shows existence) is a lot different than saying "I am a cat." ("am" shows equality... I = a cat)

I asked this exact question recently. I'm glad I'm not the only beginner! https://www.italki.com/question/353835