what's the difference between to answer and to reply?

Question

Answer

What is your name?  -  Elisabetta Donato.  This is an answer.
If i send you an email, you have to reply.

Answer

Both can be used. You may use either when you want a response from something. Often a reply is something written but an answer can be given in different ways (voice or words).
Answer a --- question
                      email
                      telephone
reply to --- a question
                   an email
                   a message