The word master isn’t exclusively used to describe the Headmaster.
In some British schools, the term master is also used to describe any male teacher. It’s somewhat archaic, but that’s presumably the term Snape is using, which is consistent with his status. Quoting from the Wikipedia page for schoolmaster:
The word schoolmaster, or simply master, formerly referred to a male school teacher. This usage survives in British independent schools, both secondary and "preparatory", but is generally obsolete elsewhere.
It’s not a spell per se, merely an attempt to “intimidate” the map into divulging its secrets. Given that it’s probably a student-made object, I’m not sure what he thinks this will achieve, but being a teacher certainly carries status and authority within Hogwarts, and certain parts of the school might recognise that and behave accordingly.