Every messenger is a prophet but every prophet isn't a messenger. There were thousands of Nabi's but 300+ Rasools.
"The people used to be one community when God sent THE PROPHETS as bearers of good news, as well as warners. HE SENT DOWN WITH THEM THE SCRIPTURE, bearing the truth, to judge among the people in their disputes" 2:213.
"God took a covenant from the PROPHETS, saying, "I will give you the SCRIPTURE AND WISDOM. Afterwards, a MESSENGER will come to CONFIRM all existing scriptures. You shall believe in him and support him." He said, "Do you agree with this, and pledge to fulfill this covenant?" They said, "We agree." He said, "You have thus borne witness, and I bear witness along with you." 3:81
I do not know authenticity of numbers you mentioned but as far as I know, concept you mentioned is right. Here is what I know:
Nabi = Prophet ... Rasul = Messenger ... All Rasul are Nabi but all Nabi are not Rasul.
Both Nabi and Rasul are chosen people (by birth) and they are sent to this world with mission that is to guide masses around them in following Shariah. Anyhow, if they are Nabi and not Rasul than they would not bring new message but would guide people in following existing Shariah. If they are Rasul than along with guiding people, they would bring new message from Allah or bring message from Allah that is renewal of old message or addition to old message (It is not necessary that a Rasul will bring new Shariah).
Rasul/Nabi can come for their own family members, for extended family members, for their community (that includes extended family members plus people living around them). Anyhow, Prophet (SAW) was only Nabi/Rasul who came for whole humanity.
For Instance:
Ibrahim (AS) was Rasul and his message was not for community but for his own family members (him and his descendents).
Musa (AS) and Prophet (SAW) were Rasul who brought message and new Shariah with them. Difference is that, Musa (AS) brought message for his extended family members, that is, children of Yaqub (AS), grandson of Ibrahim (AS). As for Prophet (SAW), he was only Rasul (Messenger) who brought message for whole humanity.
Dawood (AS) and Isa (AS) were Rasul and brought message with them, but it was not new Shariah. Both Rasul were renewing Shariah [modifying existing Shariah of Musa (AS)] but widely were following Shariah of Musa (AS). Their messages were also for children of Yaqub (AS). It is possible that Suliaman (AS) was also Rasul as Jews claim that they have a book from him.
As for Nabi, all above were Nabi. Anyhow, apart from them above, Haroon (AS), Yahya (AS), Yaqub (AS), Yusuf (AS). Zakariya (AS), Salih (AS), Lut (AS), etc ... were Nabi as they guided people but did not bring any message from Allah.
Allah has sent many Rasuls and Nabis all over the world in every community. Unfortunately, their messages got corrupted over time by their followers hence it is very difficult to determine any particular name to be Rasul/Nabi with certainty other than names of Rasul/Nabi mentioned in Quran.