Both .qgs and .qgis files are projects from Quantum GIS and they might even be the very same file type, just with different/renamed file extension. But it is more likely that these come from different versions and qgs to qgis conversion is just attempt to produce version for some particular version of the program. Unless there are problems with backward compatibility, such conversion is usually possible via re-saving in proper version of the software.
Updated: October 13, 2022