So Mozilla is jwz's name for the Netscape code that they open sourced. Does anybody know if there is a continual code-base going back through Firefox to Mozilla to Netscape to Mosaic? In which case, they could claim, they invented it all.
jwz mentions that he was unsuccessful lobbying the release of the 3.0 source.[1] For the purposes of this discussion (since you only ask about the browser here), according to Brendan, 4 was like 3.[2] Seibel mentions there that Brendan says he tried to get it released, too. The big rewrite that everybody talks about is Gecko (under the stewardship of Gessner, I think), when 5 got ditched and the next release jumped to 6. It's still listed on the MXR homepage (under Classic). Then, ho-ho, there came another new flavor at the genesis of Firefox proper, Aviary, which is also indexed on MXR. I don't know what sets it apart from pre-Aviary besides that it ditched the old XPInstall stuff. (Yeah, XPIs still exist, but most people don't realize that's not XPInstall anymore. That's the new-ish "toolkit" install system.)
From my vague understanding of the history, Mozilla code goes all the way to Netscape. I think Netscape did a giant rewrite, so it probably doesn't go back further.
Technically, firefox is the browser front-end to the Mozilla codebase, and Thunderbird is another front-end of the same product. I think what used to be called the Mozilla suite is now seamonkey. So I think it all comes from the Netscape release.
http://en.wikipedia.org/wiki/Tabbed_browsing
You could say that Firefox brought it to the mainstream, as for many people that was the first introduction to it.