'Response' has a much wider meaning than 'answer'.
An 'answer' is a reply to a question, and is usually verbal. An answer can be 'Yes' or 'No' or 'It's five o'clock'.
A 'response' can be anything - a smile, a laugh or a punch in the face!
You can have a physical response to something, such as going pale when you have a shock, or laughing when someone tickles you. You can also have an emotional response, such as feeling angry or happy or sad. These are responses - they are not answers.