Back before Mozilla, in the days of Netscape 4, the fad was to have a big all-in-one package. The Netscape 4 Communicator suite was a browser, an e-mail client, a newsgroup reader, and a WYSIWYG HTML editor, all rolled up into one big happy package.
So when Netscape gave way to Mozilla, things started out as a single big program that did everything and had a gazillion different features and options all rolled into one. It was called the Mozilla Suite, and for a while, the Suite was Mozilla's flagship product.
Then a group of developers decided to create a new project called Phoenix (because it's Mozilla reborn) where they took Suite and started to strip out everything that wasn't related to the browser (so no e-mail client, no editor, etc.), simplified the UI (hacked out a ton of menu items, simplified the options, etc.).
Phoenix uses the exact same core/engine (Gecko) as Suite--Mozilla products run using the same core rendering engine that is used for web content. That user interface that you see? It's laid out using a markup language like XUL (not unlike Microsoft's XAML, and both bear resemblances to HTML), styled using CSS, and programmed using JavaScript. This is why Mozilla is so naturally cross-platform, since its UI widgets are all done by Gecko and are naturally OS-independent (though there is skinning to match the OS style; I had worked on code in Gecko that uses the raw widget drawing APIs in Windows to render things like buttons in the native OS style).
And along the way, they also developed a framework that ran atop the engine, that they appropriately (and not too cleverly) called "toolkit". Anyway, early versions of Phoenix was just a crudely-hacked-down version of Suite, but with each successive version, toolkit was further developed, more vestigial Suite code was removed, and more of the roughness was polished down.
Along the way, they ran into trademark issues, so Phoenix was renamed Firebird. And around that time, the old mail/newsgroup from Suite (that was cut out of Phoenix) was spun into a separate program of its own, called Thunderbird, also using the same toolkit that Firebird used. Fire/Thunderbird was codenamed Aviary (both birds).
Eventually, they ran into trademark issues again, so they decided to go wild with the name and pick something with no chance of running into a trademark issue, so Firebird became Firefox, but Thunderbird remained a bird, and the overall project was still codename Aviary.
Anyway, by cutting away all the non-browser features of Suite, Firefox was much smaller than Suite and started up faster. The UI was cleaner and tidier, and it became popular. Suite remained the favorite of some die-hard power users who liked having a gazillion features, but Mozilla Suite was never popular, and was never a challenge to IE.
Eventually, Mozilla made Firefox its flagship product and abandoned Suite, because, let's face it, most people didn't like Suite. Had Firefox never been developed and Mozilla kept using Suite, we might still be seeing 90+% IE market share today--that's how little traction Suite was getting. (And before you mention WebKit, the lead dev on WebKit was one of the original Phoenix developers that Apple poached from Mozilla, and the lead on Chrome was the Firefox lead dev that Google poached from Mozilla after Firefox 2.) Suite was then picked up by the community, renamed to Seamonkey, and its development has continued. With Seamonkey 2.0, they switched to Toolkit (the framework used by Firefox/Thunderbird), but SM is still the big hulking suite with lots of features. But since all the new features (like, say, the download manager) are being developed on Firefox, they need to backport a lot to keep features updated or to add new features (which is why they eventually went to Toolkit).
Now, keep in mind that the core (Gecko--the rendering engine, the JavaScript engine, basically anything in the code base written in C/C++) is, has been, and always will be the exact same between Seamonkey and Firefox. The difference is in the UI that runs atop that engine. Similarly, Australis is a change in the UI that runs atop that engine. Pale Moon, too, uses the same engine. Heck, even Thunderbird's engine is identical. Gecko isn't forked--all this forking and happens in the layer that sits above the engine.
So what is Seamonkey? It's basically the old-school everything-plus-the-kitchen-sink suite. With modern hardware, its bloatedness doesn't hurt as much (remember, the Seamonkey-Firefox split happened over a decade ago). It lags behind Firefox because there aren't as many developers, features that they want have to be backported from Firefox, and sometimes things are a little incomplete.
Pale Moon, however is basically Firefox. With some relatively minor (at least compared to Seamonkey) UI changes.
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