Not just was Netscape, Mozilla was straight up founded by Netscape people https://en.m.wikipedia.org/wiki/Mozilla

On January 23, 1998, Netscape announced that its Netscape Communicator browser software would be free, and that its source code would also be free.[4] One day later, Jamie Zawinski of Netscape registered mozilla.org.[5] The project took its name, “Mozilla”, from the original code name of the Netscape Navigator browser—a portmanteau of “Mosaic and Godzilla”,[6] and used to coordinate the development of the Mozilla Application Suite, the free software version of Netscape’s internet software, Netscape Communicator.[7][8] Zawinski said he arrived at the name “Mozilla” at a Netscape staff meeting.[9] A small group of Netscape employees were tasked with coordinating the new community.

I remember using Mosaic on Silicon Graohics machines back in the early ‘90s. It’s was fab for the time.

And yes, Mosaic became Netscape, became Firefox. From the wiki page at https://en.m.wikipedia.org/wiki/Netscape_Navigator

The business demise of Netscape was a central premise of Microsoft’s antitrust trial, wherein the Court ruled that Microsoft’s bundling of Internet Explorer with the Windows operating system was a monopolistic and illegal business practice. The decision came too late for Netscape, however, as Internet Explorer had by then become the dominant web browser in Windows. The Netscape Navigator web browser was succeeded by the Netscape Communicator suite in 1997. Netscape Communicator’s 4.x source code was the base for the Netscape-developed Mozilla Application Suite, which was later renamed SeaMonkey.[4] Netscape’s Mozilla Suite also served as the base for a browser-only spinoff called Mozilla Firefox.

https://en.wikipedia.org/wiki/History_of_the_web_browser ;)