When some of your email messages appear on one PC, and other messages on another, you're using the wrong protocol.

Unless a single PC provides your only interaction with Gmail, you'll be much happier using an IMAP configuration instead of POP.

Mail, the built-in email program on Mac computers, doesn't have the import/export tool incorporated into most other email programs. To transfer your email settings to your PC, you'll have to go ...

Once you have an IMAP e-mail account, all your devices will be able to read, save or delete new e-mail. Whether your old mail will be visible on all devices, or just your PC, remains to be seen.