This is a simplified breakdown of a pseudo-arabic system for ranking nobility.
Sheikh - A tribal leader.
Emir/Amir - Essentially a commander, this rank is usually translated as "prince," however, in function the position is more along the lines of clan head.
Sultan - This title applies to rulers who are not Caliphs, but rule territories known as sultanates in their own right.
Malik - Title for the ruling monarch of a kingdom, equivalent to the European rank of King. The female version is Malika.
Caliph - While essentially a religious title, the position corresponds to that of emperor, with caliphs ruling over caliphates composed of subordinate sultans and emirs.