아니, 아니요, and 아니에요 all translates to 'No'. So what's the difference between them?
아니다 means 'to be not'
아니 and 아니요 are both exclamations that mean 'no', used when answering a Yes/No question. 아니 uses the 해체 speech level; 아니요 uses the 해요체 speech level. 아니요 is often compacted to 아뇨. 아니/아니요/아뇨 are used on their own as an independent phrase.
아니에요 means 'It is not', and is the conjugated form of the verb 아니다 (to be not) using the 해요체 speech style and declarative sentence type. It is an irregular verb so you may expect the conjugated form to be 아니
다+ 어요 ⟶ 아니어요 (you may still hear this in old Korean dramas); but instead it conjugates (irregularly) to 아니에요 (perhaps to make pronunciation easier). 아니에요 can be compacted to 아녜요.
You'd use 아니에요 when:
- answering a certain type of Yes/No question where the question has the form "Is X...?" (아니에요 doesn't make sense if used for a question like "Do you want to go now?" - use 아니요 instead)
- someone thanks you and you want to say it's not worth thanking. It's short for (감사할 일) 아니에요, or 'It is not (something you should thank me for).
Here's a more complete list:
- 해체 - 아니
- 해요체 - 아니요
- It's not
- 해체 - 아니야
- 해요체 - 아니에요
- 하십시오체 - 아닙니다