An answer is a reply (an answer to a question). And also a (possibly potential) response (solution) to a problem.

A response is any kind of reaction to a stimulus. E.g. .....You can respond to an insult by ignoring it, by walking away, or by slapping the person. You can respond to a compliment by feeling embarrassed and blushing, or accepting it as your due. You can respond to a crisis by dealing with it effectively, or ignoring it, or collapsing into tears. If someone tries to rob you, you can respond by fighting, running away or giving them your money. You can respond to medicine by getting better. Bereavement is a response to the death of someone you love. A reply is a written or verbal response. If you are insulted, you can reply with a retort.

They're very similar :) ..but respond is used in science and it's more similiar to the word REACT..I'll give you an example: The pupils in your eye RESPOND/REACT to light by becoming smaller you can't say that they reply to light, that doesn't make sense at all ..also reply is used more with letters/text messages and WRITTEN things generally etc. ...I'll give you more examples of which word is best to use in different contexts: - She replied to my text message yesterday - You need to reply to that letter from your boss - She wasn't responding to any of my calls (phone calls) - My skin is not responding/reacting well to the hot weather

They're the same word.