An account is your identity with a company, a way for you to identify yourself (login). Depending on the company and your business with them, there will be other things in your account. For example, a shopping site may have a credit card on file and information about your previous orders.
An account may also exist for email so in addition to a way for you to identify yourself (login), it will have a mailbox for you and send and receive email for you. It's common to refer to this type of an account as an email address and forget that it is also an account with the company that provides the email service.
Things get more confusing when a company has you create an account with them using your email address as your user name with them. Companies often require you to use your email address as the user name for the account you create with them: your email address is unique and it is also a way for them to contact you.
It's dangerous to use example email addresses and accounts because I don't want to accidentally use anyone's real email address, but I think I have to use real companies to make a realistic example.
Let's imagine you creating your first identity on the Internet. We'll start with a free email address at a common company, yahoo.com. Let's say your name is "Enoch Root" and you are able to create root@yahoo.com as your new email address. You will NOT be able to create a "root" email address because that has special meaning to some computers so I am sure this is no one's email address.
You can now log in to mail.yahoo.com with root@yahoo.com and the password you created. You can send email and you can receive email. You have an email address to start your online life. You ALSO have an account. The yahoo.com systems will let you login as root@yahoo.com to send and receive email, but there is more associated with your account than just a mailbox. You might add a credit card and pay for more storage or for ad-free webmail. You are likely to add your phone number so you can get a code to reset your password. You may use your account to login to other yahoo.com sites for other Yahoo services. Maybe you have a stock portfolio or a fantasy football team at Yahoo.
Suppose you are moving into a new apartment and need to get Internet service for your new home. You find the web site for your local cable company and create an account with them. When you visit thecablecompany.com, they ask you for your name, your email address, and a password to use for your account. They are going to use your email address as your account username with them.
It's important to understand that even though you are typing r, o, o, t, @, y, a, h, o, o, ., c, o, and m into the thecablecomany.com web site it's just a convenience that these are the same letters and symbols as your email address. You are NOT letting the cable company login you in with your yahoo.com account. The password prompt is for a new password, you should not use your yahoo.com email address' password, it should be something unique for your new thecablecompany.com account.
So now you can use your "root@yahoo.com" username to log into Yahoo with your yahoo.com password where you can send and receive email as root@yahoo.com but you can also log in with your identical "root@yahoo.com" user name at thecablecompany.com and the password you set for thecablecompany.com to manage your new home Internet service.
As you live your online life, nearly every company will want to use your email address as your username with them, but they are just creating an account with them that happens to have the same username but has its own password with them.
From Sandy: email is like PO Box, account user and pass are key.
name @ postal address
in the real world your account information may be filed by name and postal address but it is not your postal address --- name and address are identifier in the real world