what are the popular types of government
It should be noted, in passing, that use of the word Democracy as meaning merely the popular type of government--that is, featuring genuinely free elections by the people periodically--is not helpful in discussing, as here, the difference between alternative and dissimilar forms of a popular government: a Democracy versus a Republic.
However, as with other political systems, there are different types of monarchies. The type that many of us think of as common is the absolute monarchy, in which the monarch truly has the ultimate say in matters of government. However, most monarchies in political systems today do not follow this method. Many of them, especially in the developed world, have limits.