Compare constitutional and absolute monarchies, parliamentary and presidential republics.
Under a constitutional monarchy, the power of the monarch is limited, while under an absolute monarchy, his power is not limited by anyone or anything. Restrictions under a constitutional monarchy are prescribed by the country’s Constitution. There are constitutional monarchies in which the power of the monarch is not just limited in some areas, but is formal. For example, in Great Britain, the queen is only formally a ruler, but essentially does not have any political power.
In a parliamentary republic, most of the powers are given to the parliament and the country’s government is subordinate only to it. In a presidential republic, the head of state is the president and it is he who has the executive power, while the parliament deals with the legislative side. The government of the presidential republics is accountable to both parliament and the president.