YABB SE
YABB SE, or Yet Another Bulletin Board (Splinter Edition), was founded in 2001 shortly after the 1.0 release of YABB, by Jeff Lewis and Joseph Fung, as a rewrite/port of YABB to the PHP language, because Perl wasn't commonly available on hosting environments.
It was actively developed until 2003 or so, and released under the GNU GPL license.
While the YABB SE forum community website is preserved at https://www.yabbse.org/ this has not been powered by YABB SE in some years, and is now actually powered by an instance of SMF, albeit modified under permission to cite itself as YABB SE.
SuperMod
Sometime in 2002, an unofficial release of YABB SE was made, under the name SuperMod. This comprised the latest version of YABB SE, plus around 150 mods sourced from the community, as a single monster release.
It was known for being more buggy and unreliable than YABB SE, and fell behind on security patches.
ttForum
Sometime in late 2002 or early 2003, a group took the code for YABB SE (and not even the latest version), removed all of YABB SE's copyright notices and replaced all of them with their own, 'ttForum'.
Legacy
Between these two projects, the founders of YABB SE, plus a mod author from the community felt the best approach was to create a new project that held the spirit and some of the design principles of YABB SE but under a new closed license that would not permit derived works (beyond mods and themes), which would become SMF.