Short answers, pulled from the story.
Sultan derives from the Arabic and Semitic root salaṭa, meaning "to be hard, strong". The noun sulṭān originally denoted moral or spiritual authority rather than political rule, and appears in the Quran in this abstract sense. Only later did it come to describe a sovereign ruler who exercised political power.
The Ghaznavid ruler Mahmud, who reigned from 998 to 1030 CE, is recognized as the first major figure to clearly grant himself the title of sultan. He controlled an empire over present-day Afghanistan and the surrounding region. The Seljuk leader Tughril Bey later became the first to place the title on coinage.
A caliph was the universally recognized spiritual and political leader of the entire Muslim community, while a sultan was a sovereign ruler who held political authority without claiming the caliphate. Al-Ghazali argued that the caliph guaranteed Islamic law, while the sultan exercised the coercive power needed to enforce it. The Ottoman Empire blurred this distinction in the 16th century when Ebüssuûd Mehmet Efendi recognized the Ottoman sultan as caliph as well.
Brunei, Malaysia, and Oman are the only sovereign states that retain the title sultan for their monarchs. Malaysia operates as a federal monarchy with seven sultanates. Morocco formerly used the title but changed it to king in August 1957.
Morocco's monarch Mohammed V changed his title from sultan to malik (king) on the 14th of August 1957, while retaining the subsidiary style Amir al-Mu'minin (Commander of the Faithful). The change signaled an emphasis on secular authority under the rule of law rather than the religious connotations carried by the title sultan.
In the Ottoman dynasty, women of the imperial family carried the title sultan after their given names, while imperial princes carried it before theirs. Hurrem Sultan and Hafsa Sultan, the chief consort and mother of Suleiman the Magnificent respectively, are examples. Over the course of the 17th century the title was removed from the chief consort and eventually only the mother of the reigning sultan retained it among non-imperial women.