Not quite. The founder of Netscape, Andreasson, was a primary designer of Masaic, the first graphical browsing program, which is and was a free program from whatever university it was designed at. Andreasson could see the profit potential of the Internet, and he created the original Netscape browser, with plenty of enhancements over the original Mosaic. All of the Netscapes up through 3 or 4- some, were based on the original Netscape code. Andreasson sold to AOL, and for the most part, Netscape upgrades halted at version 7. If the Netscapes after 4 or so contained Open Source code, the browser was still highly differentiated from the Mozilla that predated FireFox (slower and much more bloated).
Meanwhile, the Mozilla group also started with Mosaic as a basis, but because they continued to offer Open Source (free) distribution, I think that the original SeaMonkey Mozilla contained plenty of Mosaic code. Firefox is the enhanced Mozilla browser, and "should be" vastly superior to anything with any touch of AOL's mishandling on it.
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