Question: While reading through Surah Yasin, I was wondering about the distinction, if any, between a Rasul and a Nabi? Many people make the argument that Muhammad (sws) was the "Seal of the Prophets", but not of the messengers. They argue that messengers will continue to come. Please clarify. 
    Answer: A study of divine scriptures reveals that there were certain persons in the past through whom the Almighty chose to guide mankind by directly being in contact with them. Each of them was called a "Nabi" (one who delivers a message or some news). The Almighty elevated some of his Anbiya (plural of Nabi) to a higher position called "Rasul". The Qur’an makes a clear distinction between the two: The extent to which a Rasul unveils the truth upon his addressees is so profound and ultimate that any denial from them makes them worthy of death and destruction as a nation^*: 

Those who show hostility to Allah and His Rasul are bound to be humiliated. The Almighty has ordained that I and my Rusul shall be dominant. (58:20)

    In other words, the direct addressees of a Rasul cannot triumph over him, and they must be the losers in the end. This humiliation has various forms. In most cases, the addressees are destroyed in their capacity as a nation if they deny their respective Rusul (plural of Rasul). Take, for example, the case of Muhammad (sws). His opponents were destroyed by the swords of the Muslim believers until at the conquest of Makkah, the remaining accepted faith. In the case of Moses (sws), the Israelites never denied him. The Pharaoh and his followers however did. Therefore, they were destroyed. In the case of Jesus (sws), the humiliation of the Jews has taken the form of servitude to the Christians till the day of Judgment as referred to by 3:55 and 59:3. The  ‘Aad, nation of the Rasul Hud (sws), the Thamud nation of the Rasul Salih (sws) as well as the nations of Noah (sws), and Lot (sws) and Shu‘ayb (sws) were destroyed through natural calamities when they denied their respective Rusul as is mentioned in the various surahs of the Qur’an (See for example: Surah Qamar). 
    On the other hand, the extent to which a Nabi delivers the truth to his nation is not as much as to entail death or destruction for his addressees. Consequently, the nation of a Nabi is not destroyed or humiliated even if they deny him. For example, the nations of Dawud and Idris who were Ambiya (plural of Nabi) were not destroyed when they denied them. 
    In other words, Nabi (Prophet) is a general cadre and a Rasul (Messenger) a special one. As such, every Rasul is a Nabi but this is not true vice versa. This is like saying that all Generals are army men but all army men are not generals. When the Qur’an says that the institution of Nabuwwat (Prophethood) has been terminated, it means that the institution of Risalat (Messengerhood) has also been terminated since the closure of a general cadre automatically means that the upper ones have also been terminated. If the above example is taken, we can say that if there is no army then there are no Generals of course. 

^*. To understand why a nation is humiliated and destroyed when it rejects its Rasul needs some elaboration: According to the Qur’an, God's purpose in endowing life to people is to test whether they accept and uphold the truth when it comes to them. A Rasul is the final authority on this earth about matters which pertain to the truth. No other person can illustrate and explicate this truth in a better manner. He uses his extraordinary powers of intellect and reasoning to deliver and disseminate the truth revealed to him. He exposes the truth in its ultimate form after which people can have no excuse but stubbornness and enmity to deny it. Consequently, if they deny the truth unveiled to them in its purest form by no other a personality than a Rasul, then there is no possibility whatsoever that a further extension in life can induce them to accept it. It is at this juncture that the Divine law sanctions death and humiliation for them.