It's more complicated than that when you're using an email client. Email as originally designed (SMTP) is uploaded to a server by a sender and downloaded to a recipient by a client (and usually cleared off the server in the process, since it was designed for mutli-user systems with hilariously limited space by todays standards), this is still very common for eg ISP based email accounts. Email as its used today ( the "webmail" / gmail approach) can be done in two fashions, either downloaded by a client like it was old email (but usually not clearing the server) in which case it's stored on the computer or "synched" from the web when you look at in the client, when this happens all that's "stored" on the computer for most messages is the meta data in the header (sender, receiver, title , does it have a read receipt / attachment / priority marking basically). but of course when the email is looked at the contents is downloaded to the computer (so you can read it) generally that information will also be cached on the computer so it doesn't have to be redownloaded / you can look at it offline but it may be deleted from the cache if it goes unused for a period of time.
If you're using webmail via a web broswer you'll anything you looked at recently in your browser cache unless you cleared it.