after Ali was murdered the bloodline of the prophet died
Not really. Muhammad had other children, most prominently Fatima, from whom the Fatimids claimed descent.

one who recognised the new leadership and those who didn't
It wasn't necessarily about the new leadership, it was about how the new leadership was appointed. The proto-Sunnites believed that the Ummah should elect the successor, and the Shi'ites believed that Muhammad had appointed 'Ali to be his successor.

it has always runned very deeply but they agree they are of the same religion.
Yes, but that doesn't necessarily grant Shi'ite clerics authority over Sunnites.