Mail Sharing

Mail is generally not shared unless you have shared the folder it belongs on in some fashion.

IMAP accounts allow for accessing Mail from a single server on multiple devices.

Exchange does the same thing.

POP by default limits the downloads to your local Users -> yourname -> Library -> Mail and Mail Downloads folder.

IMAP and Exchange accounts on Mail can store messages there if you create a folder "On My Mac."

Keep in mind if you are in need of reaching those messages while on a different device, you won't be able to unless the actual folder is shared with the other devices, and that backup of those messages is done by you to when cloning to an external hard drive, or copying the relevant Finder folders, and not your Mail internet provider.