Difference Between a Prophet & a Messenger

Messengers have greater responsibility than Prophets

A messenger (rasool) is the one to whom prophethood was gifted and he also received a new law and a book from Allah ﷻ. However, a prophet (nabi) is someone gifted with prophethood but did not receive a new law and a book. In many instances a prophet is also, someone who confirms and teaches the law previously revealed to a messenger. For example, Prophet Musa (Moses) (alaihi salaam) was a messenger (rasool), a prophet (nabi) but Prophet Haroon (Aaron) (alaihi salaam) was only a prophet (nabi) and that is because the former was revealed a book (Torah) in addition to prophethood while latter only received the title of a prophet and he confirmed and taught the book revealed to Prophet Musa (a.s). This informs us that every messenger is a prophet but not every prophet is a messenger.
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Additionally Quran brings another very important difference to our attention. As per Islamic scholars, a messenger is someone whom Allah ﷻ divinely protects until he has not completely delivered the message as opposed to a prophet whom even though Allah ﷻ has sent as a warner and guide, does not provide such protection: (Al Quran 37:171-173) Our Word has already gone forth to Our servants, the messengers, that they would surely be helped, and that Our forces will certainly prevail - For instance the case of Prophet Yahya (John the Baptist) (alaihi salaam) and Prophet Zakariyya  (Zacharias) (alaihi salaam), both were prophets and their enemies among the Jews succeeded in killing them. Prophet Isa ibn Maryam (Jesus son of Mary) (alaihi salaam) was a messenger, who delivered the Injeel (Gospel) and while they tried to kill him as well, Allah ﷻ saved him by raising him alive: (Al Quran 4:157-158) and (the Jews) said, “We have killed the Messiah, Jesus, son of Mary, the Messenger of God.’ They did not kill him, nor did they crucify him, though it was made to appear like that to them; those that disagreed about him are full of doubt, with no knowledge to follow, only supposition: they certainly did not kill him. God raised him up to Himself. God is almighty and wise.”[1] It is essential part of Islamic faith that Isa ibn Maryam (a.s) has not died and in fact will return to earth as a follower of Prophet Muhammad ﷺ and fight and kill the false messiah called AntiChrist (Masih Al Dajjal). Hence, his mission remains unfulfilled. Moreover, not only does Allah ﷻ provide divine protection to a messenger until he has delivered the message, in fact, in the case of a nations persistent disobedience, the warning of a punishment also comes to fulfillment against them either during the lifetime of that messenger or after his passing away: (Al Quran 10:47) Now every community has had a messenger; and only after their messenger has appeared [an delivered his message] is judgment passed on them, in all equity; and never are they wronged.”[2] After Allah ﷻ had raised Prophet Isa (a.s) alive, the children of Israel were attacked in 70 CE by Roman army under General Titus who entered Jerusalem and put thousands of Jews to death. The event is called the Second Temple in Jewish history and resulted in their complete banishment from the holy land for almost 2000 years. This was a divine punishment they experienced as a result of continuous disobedience to Allah ﷻ, murdering his prophets and disbelieving and attempt to murder messenger Isa ibn Maryam (a.s). This very important difference between a Prophet and a Messenger is quite evident because a messenger has greater responsibility to fulfill for which he is divinely assisted until he has not completed his mission.

References:
[1] Al Quran 4:157 – 158
[2] Al Quran 10:47 – Asad Translation.