what is the xxx.static.linuxgccrelease?

Neither.

The two component name ("xxx.linuxgccrelease") is just an alias for whatever three component name was last compiled. If the only two versions in your bin directory are xxx.static.linuxgccrelease and xxx.linuxgccrelease, then the xxx.linuxgccrelease will be equivalent to the xxx.static.linuxgccrelease version.  (The "static" simply mean it's been compiled with non-dynamic libraries, which helps when you're moving the program from one computer to another.)

To do an MPI run, you need to compile with MPI support, which ends up with an "mpi" in the second position (e.g. xxx.mpi.linuxgccrelease). We don't provide a precompiled MPI version because MPI compiles are *highly* dependant on your system, and which MPI library your computer is using (there's a bunch of them, and a bunch of different versions).

I believe that you should already have everything you need to compile for MPI in the download you have.  See https://www.rosettacommons.org/docs/latest/rosetta_basics/MPI and other posts on the forum about compiling MPI for details, but basically you'll need to edit the site.settings file in Rosetta/main/source/tools/build/  to tell the build system where your MPI libraries are located, and which MPI compiler you want to use. Sometimes just copying site.settings.killdevil to site.settings will work, but other times you'll need to make adjustements. For example, see site.settings.tacc.stampede or site.settings.piranha or site.settings.vaxmpi for examples. (The site.settings.xxx files are ones which make things work on the clusters Rosetta developers normally use.) If you've set the site.settings file up correctly, then you just need to add "extras=mpi" to the scons commandline to launch an MPI-mode compile. This should put xxx.mpi.linuxgccrelease programs in your bin directory, which is what you'd use with  the mpiexec command.