How does Mozilla Thunderbird compare with Gmail?
They're different. Gmail is housed by Google so your e-mails are stored on Goodle servers, not your own PC. The same is true with Hotmail or Yahoo mail. Most people have internet access through an ISP (your cable company, DSL company, etc.) and the e-mail is housed on their servers.
What Outlook, Thunderbird, Calypso and other programs do is allow you to access those e-mails quickly and store the e-mails on your own PC. My present ISP is Clear who is actually subleasing server space from Google. I also have Gmail, Yahoo and Hotmail accounts for various purposes.
What Thunderbird does is, in one command, check all your e-mail accounts and downloads them to your PC where you can read them and store them yourself plus lets you keep a universal address book on your PC where you can send e-mails to anyone in the book to any of the e-mail accounts you subscribe to.
If your internet is always connected (such as cable modem or DSL), you can also program Thunderbird to be "always on" where it automatically checks and downloads e-mails when they are sent to you.
It is also a good idea to have an anti-virus or two scanning your e-mails and set up some anti-spamming options.