Every major division within Shia Islam is a dispute about a particular succession.
Zaydis, named for Zayd ibn Ali who died in revolt against the Umayyads in 740, hold that the Imam must be a learned descendant of Ali through Hasan or Husayn who publicly claims the office and rises against injustice. There is no designation by text alone, no infallibility, and no hidden Imam. Zaydism accordingly regards the first caliphs as legitimate rulers even while holding Ali the most excellent candidate, which places it nearest to Sunnism; its historical base is highland Yemen, where Zaydi imams ruled intermittently for a thousand years until 1962.
Ismailis separated over the sixth Imam's succession in the eighth century, following Ismail rather than his brother Musa. They built the Fatimid caliphate in Egypt, founded Cairo and al-Azhar, and developed an elaborate esoteric theology in which the Imam discloses the inner meaning of revelation. The Nizari branch has a living, present Imam, the Aga Khan; the Bohra communities of India follow a line of missionary heads in the absence of their Imam.
Twelvers, the large majority, follow the line to the twelfth Imam, held to have gone into concealment in 874 and to remain alive and hidden until his return as the Mahdi.
Alevism in Anatolia and Alawism in Syria venerate Ali beyond what other Shia traditions do, and both stand at the edge of, or outside, what other Muslims recognise as Shia Islam; their own communities differ over how the boundary should be drawn.
The comparative point worth noticing is that these are not disagreements about God, revelation, prayer or law in the first instance. They are disagreements about legitimate authority, and they generated distinct theologies afterwards, in something like the way Christian divisions over the papacy generated doctrinal systems around an originally jurisdictional question.