Madshi means "Global" as in the Global\ prefix which you prepend to the file mapping name allowing it to be accessible in any session. Global\MappingName prefix is GLOBAL and no session numeric is ever prepended. At the system level it becomes \BaseNamedObjects\MappingName (in the case of NtCreateSection). Without the Global\ prefix MappingName is then session specific, whichever session CreateFileMapping or NtCreateSection is called in will have that session # prepended to the name like this \Sessions\1\BaseNamedObjects\MappingName
So no, OpenGlobalFileMapping is just opening whichever mapping name you specify and prepending the Global\ prefix before opening it. It is not looping through any open sessions to search for non-Global session specific objects and trying to open them. What if you had "MappingName" created in 2 different sessions, which one would be the correct one to return? This doesn't happen with truly Global session objects

P.S: Just ran a quick test with OpenGlobalFileMapping and it calls OpenFileMappingW() first with Global\MappingName then if it doesn't exist it tries without the Global\ prefix which would return the calling process' session object, if the name exists of course.
--Iconic