You can distinguish the single email message (retmesaĝo aŭ retletero) and the email service in general (retpoŝto), as you can distinguish a letter and the mail service with snail mail.
And be careful: it is RETpoŝto, from reto (= net), not from tero (= earth).
Let me see if I got it right ... "retmesaĝo" is the message, the content, while "terpoŝto" is the issuer, the sender which could gmail, hotmail, yahoo... please, someone tell me if I'm on the correct track!
You wrote 'while "terpoŝto" is the issuer' but you meant retpoŝto. Otherwise you match what the notes say.
I'm not saying that you can't, because I don't know Esperanto well enough to say that it's wrong.
Having said that...accepting only "email" would be right. Not all email goes over the internet. There are networks, which have email systems, which are not connected to the internet.