What is the difference between "Amir al-Mu'minin" (Commander of the Faithful) and "Sultan"?

Amir al-Mu'minin: A title given to the general Caliph of the Muslims. The first to be titled with it was Umar ibn al-Khattab, may Allah be pleased with him.

Sultan: A title given to a person in authority who is below the rank of Caliph. The first to be titled with it was Mahmud ibn Subuktigin al-Ghaznawi, who died in the year 422 AH.