The verb 'to respond' and the noun 'response' are more general than the verb 'to answer' or the noun 'answer'.
An answer is a type of response. An answer is usually verbal ("Yes", "No", and so on) and is a reply to a question. For example, if you say 'What time is it?' and I say 'It's 3 o'clock', this is a question and an answer.
A response doesn't have to be verbal, and a response doesn't have to be a reply to a question. For example, if you smile at someone and they smile back at you, this is a 'response.' It isn't an answer.