What are the differences between parliamentary and presidential systems of democracy?

The fundamental differences between parliamentary and presidential democratic governments lie in the process by which heads of government are elected/appointed, the nature of cabinet selection, to whom governmental leaders are responsible, relationships between executive and legislative branches, and basic functions.

First, in a parliamentary government, executive selection is a result of appointment by the head of state and the individual appointed is typically selected from the largest party within parliament to ensure that fundamental goals...

The fundamental differences between parliamentary and presidential democratic governments lie in the process by which heads of government are elected/appointed, the nature of cabinet selection, to whom governmental leaders are responsible, relationships between executive and legislative branches, and basic functions.

First, in a parliamentary government, executive selection is a result of appointment by the head of state and the individual appointed is typically selected from the largest party within parliament to ensure that fundamental goals of parliament are upheld. In a presidential regime the executive is elected by the people for a specific term; in the United States said term is four years and there is the potential that the executive can be reelected to serve a second term. Thus, in a parliamentary system each election has the potential to change which party is in control whereas in a presidential system elections themselves have said power unless Congress chooses to impeach the president or until the next election. Parliamentary systems may also hold elections at unscheduled times, unlike presidential elections, which occur at specific intervals. Furthermore, in parliamentary systems the entire constituency does not have the capacity to vote for the executive by name (except in Israel), while in presidential systems the entire country does have the opportunity to vote for the potential president by name (even though, as is the case in the United States, the electoral college essentially bypasses popular vote based on state population). In parliamentary regimes the head of government and head of state are usually not the same person; however, in presidential regimes one person holds both roles.

With respect to elections, in presidential systems the two primary parties (Democrat and Republican in the United States, for example) have the most power and a vote for a marginalized third party such as Independent, Libertarian, etc. is typically a wasted vote. In parliamentary systems, however, minority groups can create other parties and they have considerable influence with respect to existing coalitions.

A second difference involves cabinet appointees. In parliamentary systems the prime minister appoints ministers who can be personal choices or a result of coalition bargaining among parties. In presidential systems, however, the president appoints department heads but Congress must consent to said appointments. Relatedly, the cabinet in parliamentary systems is, essentially, an equal to the prime minister with the ability to exert considerable influence; however, in a presidential regime the president is the sole executive with cabinet members subordinate to him/her.

In parliamentary systems where the head of state and the majority party are aligned, the ruling party gets to govern the way it wants and pass whatever laws it desires. However, in presidential systems the legislature and executive often work against each other thanks to the inherent checks and balances systems to limit what the government can actually accomplish, and there is often sabotage by one party against another, especially when the president and legislature are of different parties, as is oftentimes the case in the United States.