What is the difference between Prophets (Anbiya) and Messengers (Rusul), and who are the Prophets mentioned in the Qur'an who were not Messengers?

The difference between a Prophet (Nabi) and a Messenger (Rasool): A Messenger is one to whom a law is revealed, and he is commanded to convey it, while a Prophet is one to whom a law is revealed, but he is not commanded to convey it. The correct view is that a Messenger is sent to a disbelieving, denying people, whereas a Prophet is sent to a believing people who already follow the law of a Messenger who came before him, to teach them and judge among them. Twenty-five Prophets and Messengers are mentioned by name explicitly in the Holy Quran. Among them are Prophets who were not Messengers, such as Adam, Isaac, Jacob, and Joseph. They are Prophets because they followed the law of those who came before them, just like Aaron, Jonah, David, Solomon, Elijah, Elisha, Zechariah, and John, who ruled according to the law of Moses, peace be upon him.