Answer
In this fatwa:
A Prophet refers to someone who Allah inspires, whereas a Messenger, besides inspiration, is also bestowed a mission to preach or given laws.
Responding to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
There are two terms used in the Islamic sources, namely, nabi and rasul, which may be translated respectively as prophet and messenger.
A Prophet refers to someone who Allah inspires, whereas a Messenger, besides inspiration, is also bestowed a mission to preach or given laws. So every Rasul is a prophet, while not every Nabi is not a Rasul. We learn from a tradition attributed to the Prophet (peace be upon him) that there were altogether 124 thousand prophets, while there were only 315 messengers.
There are five Great Messengers mentioned in the Quran, namely, Nuh, Ibrahim, Musa, `Isa, and Muhammad (peace be upon them all), and the Prophet Muhammad is the seal of prophets and messengers, after whom there is no other prophet to come.
Almighty Allah knows best.