Muhammad (peace and blessings of Allah be upon him) is the Seal of the Prophets and Messengers

The scholars (may Allah have mercy on them) differed concerning the difference between a Prophet and a Messenger. The majority of scholars are of the view that a Prophet is one who received Revelation from Allah but was not commanded to convey it, whereas a Messenger is one who received Revelation and was commanded to convey it. 

But despite this difference of opinion, they are unanimously agreed that a Messenger is superior to a Prophet, and that a Messenger attained the honour of Prophethood and more. Hence they said: Every Messenger is a Prophet, but not every Prophet is a Messenger. 

Thus it is clear that everything which says that the Prophet Muhammad (peace and blessings of Allah be upon him) is the Seal of the Prophets and that there is no Prophet after him indicates that there is no Messenger after him either, because there cannot be any Messenger who is not also a Prophet. 

If the text said that the Messenger Muhammad (peace and blessings of Allah be upon him) is the Seal of the Messengers, that would not suggest that there would be no Prophet after him, because it would be possible for there to be a Prophet who was not a Messenger.  

But, the text states that the Messenger Muhammad (peace and blessings of Allah be upon him) is the Seal of the Prophets and that there will be no Prophet after him and this means that there can be no Prophet after him and no Messenger after him. 

Ibn Katheer (may Allah have mercy on him) said: 

“but he is the Messenger of Allah and the last (end) of the Prophets” [al-Ahzaab 33:40]. This verse states that there will be no Prophet after him, and if there will be no Prophet after him, then there can be no Messenger after him either, because the status of Messenger is higher than the status of Prophet; a Messenger is also a Prophet but the converse is not necessarily the case."(Tafseer Ibn Katheer  3/645). 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: If he was the Seal of the Prophets then he was also the Seal of the Messengers for sure, because there is no Messenger who is not also a Prophet. Hence it is said: Every Messenger is a Prophet but not every Prophet is a Messenger."(Majmoo’ Fatawa Ibn ‘Uthaymeen  1/250). 

And Allah knows best.