First, some history: when the original hackers behind NCSA Mosaic left the public sector to form Mosaic Communications, they had a vision of a new, powerful version of Mosaic that would take the world by storm. They codenamed it Mozilla. The NCSA and its parent, the University of Illinois, quickly nipped the Mosaic naming in the bud, and soon the name of both product and company was Netscape. Mozilla became the name of the cute lizard-y mascot that ran all over the web site... and it also remained in the user agent string that identified the Netscape browser to the world's web servers.
Many years later, Netscape made the decision to release its browser code under an open source license. However, to do this and still honor its code-licensing agreements with people like Sun (this was back when Java in the browser still mattered to people) and RSA (this is also back when the patent on the RSA encryption algorithm hadn't yet expired), Netscape also needed the ability to create a separate version of its browser, incorporating closed-source code.
They created the Mozilla Public License, which reads much like the familiar General Public License, with the added stipulation that the copyright holder (in this case, Netscape) may release contributed code in an alternate version of the package which also contained closed-source code. In theory, this allowed Netscape to keep pace in the browser wars by not having to develop all-new Java and encryption code, or by simply allowing some old portions of code to survive while slowly incorporating new, open-source material. There would be a completely open-source product called Mozilla, as well as a more stable, mature (and corporate) version properly called Netscape.
In practice, though, the Mozilla coders saw fit to completely overhaul the browser's technical infrastructure, and Netscape had little that it could incorporate into a stable corporately-branded product for a long, long time. But eventually, the maturity of the purely open-source Mozilla codebase caught up with that of Netscape, and even surpassed it.
Just a short while ago as of this writing, Netscape's parent company AOL laid off almost all of its remaining browser coders and announced the formation of the Mozilla Foundation, a truly independent, non-profit entity that would oversee Mozilla development. Current builds of Mozilla are earning raves for their stability, security, and innovation in a space everybody thought couldn't be improved in user-interface terms. Netscape, the browser, stands at version 7, having skipped a number a few years ago... and will now likely never see another release. All the new browser and mail-client functionality will be going into Mozilla.
So, to answer your question, the difference is that Mozilla lives, and Netscape is dead.
