Nubuwa - reception (Given a book from God to humans) (doesn't include hadith qudsi, that is hadith qudsi not included in Nubuwa)
Wahyi - revelation (chosen receive it like Mariam and of course his Anbiya, but so can non-chosen like God talking to Pharaoh in Quranic recorded event)
Resalah - Message (chosen to deliver clear conveyance of certain messages from God to minds of people, the messages from God can be paraphrased in own words to convey and this is different then Nubuwa which is direct book from God to be held on to as scripture, that is Nubuwa is purely receiving that and giving that reception)
Now since Quran is conveyed and has clear message, it can be said to be a Resalah. If it's the case all books from God are a clear message to humanity and this is true, then every Nabi is a Rasool but not every Rasool is a Nabi.
However, since, we can imagine Nubuwa that doesn't have to be a clear message but is additional wisdom and compliments clear message already among the people, we may argue, in this condition, a Nabi is not necessarily a Rasool (if his Nubuwa is just building what is already clearly conveyed, and the scripture is supplementary, but not necessary to convey the truth).
So now we see not every Nabi is necessarily a Rasool and not every Rasool is necessarily a Nabi. However rationally, we can deduce 99.9% of Rasools are Anbiya and 99.9% of Anbiya are Rasools. This is because of how books of God function to society continuously God speaking to humans is beneficial, and Rasools are almost always needed become seldom does a society agree on truth and not dispute it and submit to God and are enlightened.
Amr in Quran refers to Authority and Mulk is used synchronously with it and seem to me to mean the same thing in context of Quran almost in every place, there is of course exceptions, but in most cases it's the same. And it's used in a way to preserve what God meant by each as both of these can be translated differently. This concept is used to show Messengers for example where Divinely appointed Kings by God.
Imama in Quran doesn't refer to what Shiites think, but is in fact used in context of inspirational leading type by example type leadership, a person who is meant to be looked for for light. Now because the example includes inward states, God emphasize Imamate in four places in this respect:
1] No oppressor can be part of the one entrusted to be followed by all humans (Suratal Baqara) and this is used to show, that humans need a leader now, and so it proves Mohammad (s) to the people of the book especially since it reminds of Ismail and the promise in his offspring with respect to Abraham.
2] In Suratal Furqan, it's put the contentions of Mohammad's people against him and among the criticism is that he was human and walked in the markets, and then in response reminds of who God's servants (that he chooses for his religion are), it goes on to give them characteristics and then reminds they sought to be leaders for the pious and from their offspring what cools their eyes. This surah also reminds of Aaron and his position to Moses, and we see Moses' pray regarding his leadership so this is nothing odd.
3] In Suratal Anbiya - Mariam is included which shows Sarah and Fatima have this type of leadership. It's the type of being light and inspiration to humans in both the physical world and spiritual world and so Fatima is a leader in this sense and it's emphasized they lead by God's command and he revealed/inspired them good works.
4]In Suratal Sajda, it's emphasized to reflect over God's guidance in three forms (proving examples of destroyed nations and his way, a book from him, and thirdly leaders who guide by God's command when they were patient and sure of God's signs - it's shown bani-Israel had all these three from God but yet deviated)
As far Mulk and Amr goes because it includes the right of being looked to and referred to for all political affairs as well, it's a bit different.
Naqeeb in Quran refers to a concept of ship by the name of God and this means all affairs of humans they are to be looked to, and so doesn't include Fatima and Sarah and Mariam.
All these are emphasized in Quran. The only one said to come to an end is Nubuwa. So there is no rational basis to conclude an end for the others and in fact, by singling out only to end Nubuwa, and not declare the others have ended, you can say they have not.