Dear questioner, thank you for your interesting question. We will try to clarify to you these important concepts and other related terms in Islam.

The Qur’an and the hadith imply a cohesive community of the believers in the message of Islam preached by the Prophet Muhammad (peace be upon him). The expressions ummah, millah and jama`ah convey this sense of cohesion since these terms are nowhere employed in the Qur'an and the sunnah.

The great objective that Islam comprises is the creation of a new type of relationship between the Creator and the creature and transformation of this bond into the life of the people in order to build a healthy social structure. It also wants to create a wholesome atmosphere in which peace reigns supreme, and offers the fullest opportunity to the individual to discharge his obligations to God as well as to his fellow beings. Islam wants to create conditions in which man is enabled to develop himself morally and spiritually.

In order to achieve these social and moral objectives, the Prophet (peace be upon him) has given instructions which are meant to transform Muslims into an orderly and well-knit society under a chief having distinctive qualities. He looks after their needs and interests. He is elected in the light of broad and flexible principles laid down by the Shari`ah. If he is the supreme administrator, he is known as Khalifah or Amir-ul-Muminin or Imam but if he is a deputy nominated by the head of state or a locally elected executive to enforce the laws of Shari`ah, or to act as a judge in their disputes or to organize the community's religious life, he is called an Amir.

The election of the caliph is a religious obligation that is so grave and urgent that all those companions of the Prophet who loved him most including Abu Bakr and members of the Prophet’s household gave it precedence over the burial rites of the departed Prophet (peace be upon him). The same procedure was followed after the death of almost all the subsequent caliphs. Ever since the election of Abu Bakr as the first caliph in 10 AH/631 AD to the martyrdom of the Abbasid Caliph Al-Mu`tasim Billah in 656 AH/1258 AD the world of Islam never remained without a caliph except for a short period of three months and seven days when Caliph Al-Mustarshid Billah was imprisoned on the 10th of Ramadan 529 AH/ 24th June, 1135 AD by the Saljukid Sultan Mas`ud. But it was such a shocking and lamentable experience for the Muslims of the day that the whole city of Baghdad felt dejected and disconsolate.

I hope this answers your question. Please keep in touch.

Salam

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Source: www.en.alukah.net with modifications.