Malaysia has an elected monarch. The kings of other regions within the country vote for the overall king. Iran is ruled by Theocracy. This means that the government is run by the religious leaders of the people. Ireland is a Republic.
Many republics have two elected leaders, usually a prime minister and a president.
The prime minister holds all the power while the president is a symbolic figure with little power. Iraq is an example of Dictatorship. This is when an individual or small group of individuals seize and hold power. No opposition is allowed. China is an example of a Communist country.