What's the difference between anieyo and anida?
아니다 = the dictionary form of the descriptive verb meaning "to not be"
아니에요 = polite conjugated form of 아니다 (like: "I am not a teacher. / 저는 선생님이 아니에요.)
And in case you were asking about 아니요 ...
아니요 = No (a negative affirmation in response to someone. Like, "No, I don't like xyz." / "아니요, 치킨을 싫어해요.")
That's what I was taught too but someone used 아니다 as "그는 학생이 아니다" which I thought was supposed to be "그는 학생이 아니에요." So naturally, I was just a little confused but thank you.
Since 아니다 is a descriptive verb, 아니다 is actually a valid conjugation as well -- it's called the "plain form". In plain form, descriptive verbs don't change, but action verbs get the ㄴ/는다 conjugation. So the sentence was probably in plain form.