Parliamentary democracy is the type of government where the public vote government into power and parliamentarians are representative of the people. While a Presidential Democracy is when there is a system of government that has a president acting as the nationâs head of state and active chief executive authority. The similarities between the Presidential and Parliamentary model are: both are representative democracies, both have a head of state, both have a bicameral form of government and both are rule by constitution. There are also differences between the Presidential and Parliamentary model.