The historical inspiration for Assassin's Creed's medieval Assassins is the Nizari Ismailis.
The Nizari Ismailis were a branch of Ismaili Shia Islam whose medieval strongholds included Alamut in Persia and mountain fortresses in Syria. Western sources often called them “Assassins,” a term connected to the popular history of their enemies and later legends about targeted killings.
The video-game Brotherhood is not a literal historical portrayal of the Nizari Ismailis. Ubisoft combines the historical inspiration with fictional doctrines, characters, artifacts, and a continuing conflict against the Templars. Altaïr's missions take place during the Third Crusade, but the game's hidden organization is designed for a broader fictional saga.
The Knights Templar are a separate medieval organization and serve as the game's principal opposing order. Confusing the two reverses the basic historical inspiration: the Assassins draw from the Nizari Ismailis, while the Templars are based on the real Catholic military order active during the Crusades.