But both the constitutional king, under a limited Monarchy, and the President of a Republic, exercise authority as ordained by the Constitution or conventions as in Britain.
They cannot go beyond it. In a limited Monarchy the authority of the long is nominal. The real functionaries are his ministers who are elected members of the legislature and belong to the majority party. They remain in office as long as they can command a majority in and retain the confidence of the legislature.
They cannot be dismissed by the king at his pleasure. Nor can they be chosen at random. Britain is a typical example of a constitutional Monarchy where the King or Queen reigns but does not rule.