Bahgdad in Iraq was the central point (politically) between the two (Arab & Persian).
Shia were formed because they were the followers of the 4th Caliph 'Imam Ali' (Mohomad's son-in-law & at same time his cousin). Hassan was Ali's oldest son, who under threat abdicated Caliphate seccession in favour of the 5th Caliph (Ummayad clan) after Ali was murdered. Ali's second son Hussayn was also murdered by the 'Sunni' - the followers of the 'loosely' elected 5th Imam 1st of the Ummayad clan. With both Ali and Hussayn having been murdered, they became 'saints' to the Shia (party of Ali). Shia regard Ali as the 1st Caliph and the true heir to Mohomad. There is a debate that still gets argued over today as to if Mohomad always intended Ali to take over directly from him. That of course didn't happen. Three other Caliphs were 'elected' before Ali got his go & Caliphs 2,3 & 4 (Ali) were all murdered as was Ali's 2nd son.
The split is not unlike that in the Mormon religion founded by the 'prophet' Joseph Smith. When Smith was lynched, the followers of Brigham Young (the equiv of the Ummayads) split (physically & figuratively) with the followers of Joseph Smith's son and trekked to Utah from Missouri.
The Mormons became two factions: Brigham Young's "Church of Jesus Christ of Latter day Saints" and the Smith son followers "Reorganised Church of Jesus Christ of Latter Day Saints". The latter stayed in the town they founded - Independance Missouri, & fought a court battle to retain the property etc: of The original church but Brigham Young's group became the Mormon powerhouse we all think of today as the 'Mormons'.
The split between the Sunni and Shia was very much (but not totally) a Persian vs Arab split with the Shia being predominantly of Persian origin. The Ummayads dominated the caliphate for many years before being overthrown by the Abbasaid dynasty (Interestingly, it was one of the survivors of the Ummayads who fled to Spain & founded the Andalusian empire there).
Both the Ummayads & Abbasaids were harsh to the Shia. The Sunnis believed in an 'administrative' and Arab dominated Islam where the Caliphs were administrators as well as heads of the religion whereas the Shia believed in a religious (spiritual) leadership with less vaue on who administered (Sunnis followed power leaders, Shia followed the descendants of Mohomad through Ali).
The Sunni/Shia split is actually very complex but in simple terms, it is as above.
Doug Marker
#2 correct sp of word Caliphate in title
#3 corrected ref to Hussayn being Ali's 1st son (he was his 2nd)