These verbs have essentially the same meaning. You can:
▶️ answer an email
▶️ reply to an email (most common when talking about e-mail)
▶️ respond to an email
When someone calls you, you answer the phone (or pick up the phone).
When you make a statement or some comments, we usually say the other person
replies or responds.
When you ask a question, we usually say the other person answers. However, this is
not 100% – reply and respond can also be used for answering a question.
When used as a noun (with a, an, the and possessive pronouns like my, your, his,
her, etc.) the words answer and reply don’t change – but the noun form of
“respond” is response.
▶️ He answered my question, but I didn’t understand his answer.
▶️ We’re waiting for a reply from the customer.
▶️ Her response to his comment was brilliant.