Please remember to use the search function in the future. A few threads for you...
http://www.tfproject.org/tfp/showthr...hlight=firefox
http://www.tfproject.org/tfp/showthr...hlight=firefox
http://www.tfproject.org/tfp/showthr...hlight=firefox
Those should provide you with MORE than enough info.
In case it's not mentioned in those, however, the primary difference between Mozilla and Firefox is that Firefox is ONLY a browser. Mozilla is a suite of applications as mentioned earlier - browser, e-mail, IRC client, HTML editor. The Mozilla browser is somewhat different than the Firefox browser, but there aren't really any significant differences that I am aware of.
To be honest, unless you're on dial-up there's no reason to not download Firefox and try it out. Seriously, it's free and fairly small, so if you're not on dial-up just do it, it's not like you can't just uninstall it. Same with the Mozilla suite, but you should be fine with Firefox unless you need that other stuff. In fact, even if you want an e-mail client as well, there is Thunderbird which is a standalone e-mail client from the Mozilla Foundation.