Both can often be used interchangeably.Originally Posted by Dany
Here's the difference as I see it:
An "answer" can be thought of as something that is short more often than as something that is extended.
With a "response" we would be more likely to expect a longer more extended answer. We might also expect this answer to be thought out to some degree.
An answer, to me, is something more direct.
A response, to me, is an answer that is more extended and that has more thought behind it.
Also, one is more likely to respond to a comment or a question, whereas one usually "answers a question". I don't think we often say "answer to a comment". We could, however, say "respond to a comment".
A "response" is also something that could indicate action, not just words. Although, we do say "answer the phone".
example: It's important for the fire department to be capable of providing quick responses to emergencies.
"response to an emergency"
Here we have "answer to an emergency". However as we can see, "response to an emergency" occurs with far greater frequency.
I would look in Cambridge Dictionaries Online or a Longman dictionary. Read up on what they have to say about "response" and "answer". You could then post some example sentences of your own. We could comment on whether or not you seem to have chosen the correct word for the context. There's some gray are here, though, as sometimes "response" and "answer" can be used interchangeably.