How does email work, and how is it different from Web mail?

You can write letters to any email addresses. mail, as well as receive letters from any email addresses.
when sent, emails go through an SMTP server, when received through a POP or IMAP server
To get an account, you need to register with your email service providers.

Web mail is implemented for the browser and only as a web application.

(E-mail can be used offline if the files are on the pc, and the web is ONLY for browsers)