Mozilla is a suite with browser, email, HTML editor and calendar all together. Firefox is a browser only, built to be lightweight and fast. All of the functions of Mozilla are now available as stand alone applications, such as Thunderbird for email, etc.
When I read about Mozilla when it first came out I kept calling it Godzilla for some reason. Sure you wouldn't have slept well tonight without knowing that very important information.
Well the same thing happened for me but I called ..... the download manager... go!zill as godzill..... sure only a difference of '!' and 'd'..... LOL
Well I've installed them both and they seem to operate in different ways. Mozilla seems to save passwords automatically better so that I don't have to type them in everytime. This is a feature I really appreciate.