presidential system is a democratic and republican government in which a head of government leads an executive branch that is separate from the legislative branch. This head of government is in most cases also the head of state, which is called president. ceremonial and executive powers are fused in a presidential system.
In a parliamentary system, the head of state is different from the head of government. Example is the UK, the head of government is the Prime Minister while the head of state is Queen. ceremonial and executive powers are separated in a parliamentary system.