Firefox is the browser component of Mozilla with a different UI. Generally I find it feels a little "lighter" than Mozilla (at least on Windows, the OS X version currently is sluggish as hell). Some options have been removed/hidden, while others are exclusive to Firefox.
It's really a personal choice thing, since the rendering engine is the same for the both of them. Also, Thunderbird is the Firefox equivalent to Mozilla's mail app.
What is Firefox exactly and why do some people recommend it over Mozilla? I have been using Mozilla since 1.3 (now using 1.7.1) and can't imagine what Firefox would do better.
Also use Mozilla Mail as default. I get the same results
on both Windows and Linux platforms without having to change anything or worry about compatibility. Been curious for a while. chuck