The first and possibly the largest difference between the presidential and the parliamentary systems is the separation of powers. In a Presidential system, there is a concise, clear separation of the three branches of the government while in the Parliamentary system there is a fusion between the executive branch and the legislature.

In a Presidential system, the President, who holds the executive power, is directly elected (in an election separate from the election of the legislature) and then appoints the cabinet of ministers – these ministers do not simultaneously take part in the legislature and, thus, there is a clear separation of powers.

This does not happen in the Parliamentary system. In this form of government, the Parliament holds the legislative power. However, the Prime Minister, who holds the executive power, also takes part in the Parliament, together with his or her appointed Cabinet of Ministers. In fact, there is only one election, in which a party is chosen by the majority of the votes to the legislature and the leader of the winning party becomes Prime Minister. There is, therefore, no clear separation between the executive and legislative branches in the Parliamentary system.
In the Presidential system, the President usually has a limit of terms in which he or she can stay in power, while in the Parliamentary system this often does not apply to the Prime Minister. However, since there a close fusion between the Parliament and the Prime Minister, the latter is dependent on the satisfaction of the former, and can be deposed by a motion of no-confidence, usually filed by an opposing party or coalition.

Furthermore, in a Parliamentary system, the head of State and head of Government are clearly separated, with the head of government often being a figurehead for the nation and either a President or a Monarch (in constitutional monarchies).

The legislative branch, in any system, is ultimately responsible for enacting laws based on an analysis of the social, economic and political situation of the country.
In the Presidential system, it can be unicameral or bicameral (which is the case of the USA, where the legislative branch is withheld by the Congress, composed of the upper body, the Senate, and the lower body, the House of Representatives) with most governments often adopting a two camera system to avoid concentration of power, with a lower house responsible for most laws and an upper house for issues of higher significance. It is the legislative branch which writes laws for the President to ultimately approve (or veto). The executive can draft or suggest laws, but it is ultimately the legislative branch that will introduce them.
In the Parliamentary system, the legislative branch is withheld by the Parliament, where the Prime Minister writes laws together with the other members of the Parliament.

The Judicial branch has a similar function and structure between forms of government. Is is withheld by courts and it is responsible for interpreting and applying laws, assuring that every accused person has the right to a fair and unbiased trial before a judge.

A hybrid system, a Semi-Presidentalist system, can be seen as inside the spectrum limited by both systems described above. They can be closer to a Parliamentary system or to a Presidential system depending on the country, with very few nuances or larger differences from these systems. For instance, the executive power can be shared between a separately elected President and a Prime Minister or the President, although not holding the executive power, represents more than a figurehead, with larger powers ranging from, for example, vetoing laws to dissolving the Parliament.