History of Muslim Rule

Total Number of Muslim Kingdoms, empires and dynasties can be found in https://en.wikipedia.org/wiki/List_of_Muslim_states_and_dynasties

Before going into discussion lets first know the difference between a kingdom, an empire and a dynasty,

A kingdom is more or less just a polity ruled by a king or some other monarch. Pretty simple.
An empire is a large state encompassing many disparate peoples and nationalities, but ruled by a single central government. If that government is a monarchy (it doesn't have to be) then that person is an emperor.
A dynasty isn't a state at all, it's a family or series of related families who held power in a state for long periods of time.

and Emirate, Caliphate and Sultanate - an Emirate is ruled by an Emir, a Sultanate by a Sultan and a Caliphate by a Caliph. Now for what those words mean and how they deviate from each other.

A Caliphate is the Islamic Nation State, the first one being Medina under the Prophet (PBUH), following this the early Umayyad Empire is probably the closest to a Caliphate there has been since. The concept of Caliphate is kind of impossible to have these days because a Caliph is a religious and political leader that is chosen by the Umma (Islamic Community), arguably since the death of Muhammad (PBUH) there hasn’t ever been a Caliph given the early split between Sunnis and Shias. If you wanted to go down either line, both lines of succession end pretty much around 100 years after Muhammad’s death when the son of Ali, Hussein was assasinated by a rival faction of Islam. Groups like Daesh claim that they are a Caliphate but without a wide acceptance of the people that is not the case, they just use that narrative to attempt to garner political and religious favour in the Umma.
An Emirate is a principality or territory ruled by an Emir. An Emir is the hereditary ruler from a line of successtion of an Islamic monarchy, so the Emirate is specifically ruled by an Islamic royal family, who percieve their rule as being the will of Allah. It can also refer to a province ruled by an Emir, as is the case in the United Arab Emirates that are Seven Emirates that work Federally. Bahrain and Qatar also count as Emirates.
A Sultanate is similar to an Emir, and exists in an Islamic context but is not explicity percieved as being a God given power, but instead the Sultan is just in the position of power. There are also regional variations between Sultan and Emir with Emirs in the modern age being restricted to the Arabian Peninsula (although there have been Emirates across Asia, Europe and Africa) where as a Sultan is a title that is rarely used today but exists in several different Islamic contexts, not just an Arabian one.

and difference between a chiefdom and kingdom,

A kingdom is a politically organized community or major territorial unit having a monarchical form of government headed by a king or queen.
A chiefdom is an autonomous political unit comprising a number of villages or communities under the permanent control of a paramount chief.

Total Kingdoms, empires, dynasties, Chiefdoms, states etc. recorded approximate to 927, some are existing till now. Which were 63 in Iran, 31 in Mesopotamia and Levant (Iraq, Syria, Lebanon, Jordan, Palestine), 179 in Middle East (Arabian Peninsula, Persian Gulf Region), 227 in West Africa (West Africa, Sahel), 64 in North Africa (Maghreb Region), 30 in Horn of Africa, 16 in East Africa, 26 in Indian Ocean Region, 58 in Southern Europe, 10 in Eastern Europe (Balkan Region), 16 in Ural Region, Siberia (Russia), 38 in Caucasus, 38 in Central Asia, East Asia, 131 in South Asia, 60 in Southeast Asia.