The Hadeeth from Imam Jafar Al-Sadiq (AS) says: Allah has made Ebrahim a servant (Abd) before making him a prophet (Nabi)), and made him a prophet before making him a messenger (Rasool), and made him a messenger before making him His Khaleel and made him His Khaleel before making him an Imam. (Al-Kafi 1/175).
This means that the responsibility of Ebrahim was increasing from Abd (servant) to Nabi (prophet), then to Rasool (messenger) then to Imam. That is why Ebrahim asked Allah whether his progeny will have the same status of Imamate? Allah replied him: My appointment does not reach to the sinners.
The prophet (Nabi) receives the revelation from Allah. The Rasool (messenger) is responsible to convey the message of Allah to people. The Imam has the responsibility to implement the orders of Allah in every aspect and every dimension of life. Ebrahim was appointed by Allah as Imam for all people to guide them all to implement the orders of Allah in life. Not all the prophets were Imams but only the greatest of them.
The Twelve Infallible Imams are not prophets but successors of the greatest prophet and greatest messenger Muhammad (SAWA). They are the divine guides who responsible to implement the orders of Allah in every matter.