They are different forms of the same verb -- you have to pick the one that matches the subject.
A bit like how you can't say "he am" or "you is" or "I are" in English: those are all forms of the verb "to be" but they're not the right one for that subject.
είμαι is the form for εγώ: εγώ είμαι "I am"
είναι is the form for αυτός, αυτή, αυτό, αυτοί, αυτές, αυτά (he, she, it, they), e.g. αυτός είναι "he is" or αυτές είναι "they are".