Is there a difference between Islam the Nation of Islam and ISIL?

Answer 1

Yes, all three refer to distinct things.

Islam
Islam, as an Established Religion, was organized and directed by Mohammed, who was born in 570 C.E. at Mecca, in Saudi Arabia. According to Islam, he received revelations from God in Mecca in from the year 610-632 C.E. He was supported by several family members like his uncle Ali Ibn Talib and his first wife Khadija to pursue these prophecies, which were eventually compiled into one unified Qur'an (the Islamic holy book). Islam is a religion that currently represents over 1.6 billion people and has several general requirements, such as the required belief and testimony that there is only one God (Shahada) and prayer to him (Salaat), that money should given to the poor (Zakaat), that a pilgrimage should be made to Mecca (Hajj), that people should reflect and fast for one month (Ramadan), and that people should rise in both spiritual and physical defense of the faith (Jihad). Most Muslims practice these general tenets along with a much more expansive Islamic Law which mandates certain benefits and punishments. Usually, these align with Western values, but in some explosive ways, they do not, resulting in numerous controversies over these legal and ethical disagreements.

Nation of Islam
Many people confuse the Nation of Islam with Islam, which is incorrect. The Nation of Islam is a specific African-American religion founded by Wallace Fard Muhammad. While Islam is not a racist religion, i.e. it does not discriminate on the basis of race, the Nation of Islam is a racist religion, holding Blacks to be a Superior Race and Whites and Jews to be Inferior Races. It makes sense that when the leadership of a religion makes openly racist statements that the religion is perceived as racist.

For example, Wallace Fard Muhammad would preach that the original humans were all black until an evil scientist Yakub created "white devil children" on the island of Patmos and proceeded to kill all Blacks until the White Devils were in power. Before Malcolm X left the Nation of Islam to become a Sunni Muslim, he said: "Thoughtful white people know they are inferior to Black people. Even [Senator] Eastland knows it. Anyone who has studied the genetic phase of biology knows that white is considered recessive and black is considered dominant." On the charges of Anti-Semitism, these come from absurd claims that the Jews were overwhelmingly responsible for African enslavement and that Hitler was a great man for murdering Jews in the Holocaust.

ISIL - ISIS - Islamic State of Iraq and the Levant
ISIL (Islamic State of Iraq and the Levant), known as ad-Dawla al-Eslamiyya al-3iraaq w'ash-Shaam (الدولة الإسلامية العراق والشام) or the acronym Daa3esh (داعش) in Arabic, is an extremist Sunni Islamist organization. It is important to clarify what Islamism is. While Islam is a religion (as described above) Islamism is a political ideology whose goal is to bring the religious tenets of Islam into the daily functioning of a government and its laws. Islamism is a modern movement whose roots began contemporaneously with the rise of Salafism in the late 1800s and early 1900s in Egypt. ISIL practices a particularly violent form of Islamism called Jihadism, which not only wishes a particularly repressive version of Islamic Law to be instituted, but believes that violence in defense of the faith is the preferred way to do this. Jihadism, like Islamism, is a political ideology rooted in Islamic religious concepts, but distorted. The distortion here is that there are many ways to advocate on behalf of the faith and the choice to exclusively use violence is a misinterpretation of the doctrine.

ISIL used to have links to al-Qaeda before al-Qaeda condemned them for their barbarity. They are fighting to bring the Sunni majority into power, especially in Sunni majority regions of both Syria and Iraq, and impose a more fundamentalist view on politics. They consider themselves to be fighting the injustices and violence of the current Assad regime and the inequalities of the US-supported Government of Iraq. ISIL is primarily supported and armed by Saudi Arabia, but the US and UK have indirectly given ISIL millions of dollars and equipment since US and UK military vehicles and assets left to the Government of Iraq have fallen into ISIL hands (especially with the fall of Mosul). ISIL controls significant amounts of land in Syria and Iraq and conquered much of its Iraqi territory in June 2014.

Summary
Islam is a religion with certain tenets.
Nation of Islam is a very different religion with different tenets.
ISIL is an Islamist paramilitary group which uses political philosophies like Jihadism to undergird its reprehensible violence.