The difference is Elder Scrolls Online doesn't have a command to run a script inline from the chat window.

So you are pretty safe unless you specifically install a compromised add on. It is definitely possible for add ons to mail stuff from your account automatically, including gold because some add ons have a "tip" feature built in, and some operate by using the mail to help you transfer stuff to a mule character. So a compromised add on could just set it up so every time you log in it automatically mails 1000 gold to another account.

But at least you would have to install the plugin explicitly instead of just compromising yourself via the chat window.