Shouldn't these two be merged (if possible) / made synonyms?
I just want to note that the two are not really the same thing.
The Windows Live label was introduced at some point and the Windows Movie Maker got a drastic overhaul, losing features and compatibility in the process. From Wikipedia:
A new version of the software, renamed Windows Live Movie Maker 2009, was released as a beta on September 17, 2008, and officially released as a standalone product through Windows Live Essentials suite on August 19, 2009. This was effectively completely new software as it could not read projects created by earlier versions and did not support custom XML transitions written for the previous versions. In addition, a great many features were removed.
An interesting thing is, the older versions of WMM are actually not WLMM, which was new and introduced with 7 (and breaks backwards compatibility with the old project files). IIRC, WLMM also has less functionality than WMM. So, they're not really the same thing.
On the other hand, with the release of 8, WLMM was renamed back to WMM - and this new WMM is different from the old XP/Vista-era one. If there's a merge/synonym at all, WLMM should go be merged into WMM, the more general and current name.
It should just be called movie-maker.