@DanR20 is about right. Moebius was forked from an alpha build of FF 53. Later on many changes were backported from FF 54 and 55; hence its identification as Basilisk version 55. (Serpent is just the name for unofficial builds of Basilisk, including @roytam1's XP builds.)
Unfortunately the PaleMoon team ran into problems with Moebius and was forced to start over with FF 52 ESR; that became Basilisk/UXP. (And again, @roytam1's XP build is Serpent/UXP.) UXP's identification is version 52.9 (although the latest versions pose as Firefox 60.9 in compatibility mode).
Main differences between the two that I've noticed are:
Moebius supports more / newer add-ons; however, it does not support most plug-ins (Java, Silverlight, Flash). Edit: if you have trouble with plug-ins see @VistaLover's post below for the fix.
Moebius still relies on Firefox sites for add-ons, sync, etc. UXP uses PaleMoon's sync and Basilisk's new add-ons page.
Both browsers get updates from @roytam1, but UXP also gets updates from the PaleMoon team. Therefore UXP is updated weekly, while Moebius is updated less often and less regularly.
Both browsers are reasonably secure but UXP is probably a bit more secure, due to the current attention from the PM team and the greater frequency of updates. Also, over time I expect Moebius will have more compatibility issues with newer Web sites (e.g., GitHub, Instagram), although it's fine for now.