'...emirs and sultans were people with political authority but NO religious authority.'
'After the death of the Prophet, the khalifa or caliph was viewed as the successor of the Prophet (which is where the word comes from). The khalifa was the leader of the Muslim community, having political and certain religious authority, and was in charge of maintaining the safety of the Muslims while ensuring that Islam would not only be preserved, but would spread. Of course there have historically been debates amongst the Muslims as to who should have been the first caliph after the Prophet, which would eventually lead into the Sunni-Shi'i split. But that's outside the scope of this response. The Khalifah was NOT viewed as having any Prophetic or Divine attributes - his religious authority came from establishing what was in the revealed text (i.e. the Qur'an) and the sayings/practices of the Prophet (the Sunnah).
'However, what is important to note is that the term khalifah was not necessarily used by the early community, or even by the caliph himself. We actually find people using terms like "emir" ("commander") more, and sometimes "imam" (leader). For instance, the second khalifah, 'Umar ibn al-Khattab, actually preferred the title Emir al-Mu'mineen (Commander of the Faithful). So for your understanding, in order to prevent any confusion, just know that in the early community we see the terms khalifah, emir, and imam being used interchangeably to refer to the same person - the leader of the Muslim community.'
So...according to this guy, a Caliph has overall political AND certain religious authority, while an Emir has only political authority and can be subordinate to the Caliph.
https://www.quora.com/What-is-the-difference-between-Emir-Vizir-Sultan-Shah-and-Khalifa
'After the first four caliphs (Abu Bakr, Umar ibn al-Khattab, Uthman ibn Affan, and Ali ibn Abi Talib), the title was claimed by the Umayyads, the Abbasids, and the Ottomans, as well as by other, competing lineages in Spain, Northern Africa, and Egypt. Most historical Muslim rulers simply titled themselves sultans or amirs, and gave token obedience to a caliph who often had very little real authority. The title has been defunct since the Republic of Turkey abolished the Ottoman caliphate in 1924.
Once the subject of intense conflict and rivalry amongst Muslim rulers, the caliphate has lain dormant and largely unclaimed for much of the past 82 years. Though many Muslims might favor a caliphate in the abstract, tight restrictions on political activity in many Muslim countries coupled with the tremendous practical obstacles to uniting over fifty disparate nation-states under a single institution have prevented efforts to revive the caliphate from garnering much active support, even amongst devout Muslims. No attempts at rebuilding a power structure based on Islam were successful anywhere in the Muslim World until the Iranian Revolution in 1979, which was based on Shia principles and whose leaders did not outwardly call for the restoration of a global Caliphate (although Iran has subsequently made efforts to 'export' its revolution to other Muslim countries).'
answers.yahoo.com/question/index?qid=20061020204856AAKq99Q no longer exists
http://cdn-cache.worldheritage.org/articles/eng/Califate