The well-known difference between a Prophet and a Messenger is that a Messenger is one to whom a law is revealed and he is commanded to convey it, whilst a Prophet is one to whom a law is revealed but he is not commanded to convey it. But this distinction is not free of problems, because a Prophet is also commanded to call people, convey the Message and judge among the people. Hence Shaykh al-Islam Ibn Taymiyah said: The correct view is that the Messenger is one who is sent to a disbelieving people, and the Prophet is one who is sent to a believing people with the shareeah of the Messenger who came before him, to teach them and judge between them, as Allah says (interpretation of the meaning):
Verily, We did send down the Tawraat (Torah) [to Moosa (Moses)], therein was guidance and light, by which the Prophets, who submitted themselves to Allahs Will, judged for the Jews
So the Prophets of the Children of Israel [were] judged by the Tawraat, which Allah had revealed to Moosa.
With regard to the aayah, but he is the Messenger of Allah and the last (end) of the Prophets [al-Ahzaab 33:40] and why it did not say the last of the Messengers the end of the Message does not mean the end of Prophethood, but the end of Prophethood does mean the end of the Message. Hence the Prophet (peace and blessings of Allah be upon him) said: There will be no Prophet after me, and he did not say, there will be no Messenger after me.
Thus we know that there is no Messenger and no Prophet after him (peace and blessings of Allah be upon him); he was the last of the Prophets and of the Messengers, (peace and blessings of Allah be upon him).