All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
The correct opinion in this matter is that there is a difference between a Prophet and a Messenger, as the Islamic texts indicate.
As regards the difference between the two, the matter is easy as there is no clear text; it is for this reason that there are various opinions about clarifying the difference between a Prophet and a Messenger. With regard to the statement that you quoted in the question, it is indeed a problem, as you mentioned, as it is not the preponderant opinion.
Dr. Umar Al-Ashqar said in his book Ar-Rusul war-Risaalaat:
“The statement of the scholars who said that there is no difference between a Prophet and a Messenger is not correct; the evidence that this statement is void is what is mentioned in regard to the number of Prophets and Messengers. The Prophet stated that the number of Prophets is one hundred and twenty-four thousand, and the number of Messengers was between three hundred and thirteen and three hundred and nineteen.
The evidence about the difference also is included in what is mentioned in the Book of Allaah, as Allaah mentioned Prophets after mentioning Messengers. Allaah says (what means): {And We did not send before you any messenger or prophet except that when he spoke [or recited], Satan threw into it [some misunderstanding].} [Quran 22:52] Also, Allaah described some of His Messengers as Prophets and Messengers; this means that the Message is something in excess of the Prophethood, as Allaah says about Moosa (Moses) (what means): {And mention in the Book, Moses. Indeed, he was chosen, and he was a messenger and a prophet.} [Quran 19:51]
The well-known opinion of the scholars is that the word Prophet is more general than the word Messenger, as the Messenger is the one to whom a legislation was revealed and who was ordered to convey it, while a Prophet is the one to whom revelation came down but who was not ordered to convey it. So, based on this, every Messenger is a Prophet, but not every Prophet is a Messenger.
But what they mentioned here is most unlikely for many reasons:
Firstly: Allaah explicitly mentioned that He sent Prophets in the same manner that He sent Messengers, as Allaah says (what means): {And We did not send before you any messenger or prophet except that when he spoke [or recited], Satan threw into it [some misunderstanding].} [Quran 22:52] If the difference between them is the order to convey, then being sent (as the verse states) does require the Prophet to convey.
Secondly: not conveying is concealing the revelation of Allaah, and Allaah does not reveal His revelation so that it would be concealed and buried in the chest of a person among the people, and then such knowledge would die with the death of that person.
Thirdly: Ibn Abbaas narrated that the Prophet said, “The nations were displayed before me; one Prophet would pass by with only one follower, and another Prophet would pass by with only two followers, and another Prophet would pass by with only three to ten followers, and another Prophet would pass by accompanied by nobody.” This indicates that the Prophets were ordered to convey and that the number of the people who followed them varied.
Hence, the chosen definition would be: The Messenger is the one to whom a new legislation was revealed while a Prophet is the one who was sent to confirm a previous legislation. "The Children of Israel were ruled by Prophets, whenever a Prophet perished, he was succeeded by another Prophet,” as confirmed in a hadeeth. All the Prophets of the Children of Israel were sent with the legislation of Moosa (Moses), the Torah, and they were ordered to inform their people of the revelation of Allaah to them. Allaah says (what means): {Have you not considered the assembly of the Children of Israel after [the time of] Moses when they said to a prophet of theirs, “Send to us a king, and we will fight in the way of Allaah”? He said, “Would you perhaps refrain from fighting if fighting was prescribed for you?”} [Quran 2:246] The Prophet, as it appears from the verse, receives revelation and then gives an order to his people, and this can only be with the obligation of conveying. This is the example of Daawood (David), Solaymaan (Solomon), Zakariyya (Zechariah) and Yahya (John); all of them were Prophets, and they were ruling the Children of Israel, judging between them and informing them of the Truth." [End of quote]
Shaykh Ibn Taymiyyah in his book An-Nubuwwaat, chose the opinion that the Messenger is the one who was sent to the people who were denying and objecting to the truth but that the Prophet is the one who was sent to the believers. He also holds the view that it is not a condition that the Messenger brings a new legislation, because Yoosuf (Joseph) was a Messenger and he was upon the religion of Ibraaheem (Abraham), and Dawood and Solaymaan were Messengers and they were upon the legislation of the Torah.
Allaah Knows best.