Maybe a thread on the various muslim denominations and sects would be informative. I confess I don't know as much about this as I should. I am aware of the big schism between Sunni and Shia and that the Shia followed Ali as spiritual successor to Mohammed, rather than Abu Bakr, and also that Sunni Islam has subsequently included sects or movements like Sufism and Wahabism, but I know little about them.
This is correct, as a vague generalization.
To explain for others:
At it's foundation, Sunnism and Shi'ism, initially are distinguished by a defining epistemic integrity which solidifies the nature of them each.
Now Sunnism's epistemic basis is around the four Madhhabs in interpretation and application, the four caliphs in terms of identity and the sunnah of Muhhamad in name (though the term "Sunni" obviously is just a term). The first Caliph, that of Abu Bakr (the father of Aisha, a late wife of Muhammad) was decided by a portion of the Muslim community via public consensus to be the first political leader following The Prophet's death.
For the most part, Sunnism is concerned with it's rich history of interpretation within it's four Madhhabs and with a specific emphasis on the companions (sahaba) of Prophet Muhammad as a reference point with understanding Muhammad through them.
Now Shi'ism's epistemic basis is also theologically and ontologically based, one axiom this is derived from the Qur'an that there in never a time on earth where there isn't divine guidance. During Prophet Muhammad's life he often made many references to Ali's (his son and law, and the husband of his daughter Fatima az-Zahra) importance to him. There are many instances of this. Nonetheless, the Shi'i view consists of an understanding that emphasizes the inward (batin) and outward (zahir) aspects of the Qur'an and in particular an epistemic understanding that the most authoritative understanding of the Qur'an comes through first Muhammad, then his Progeny.
Ali Ibn Abi Talib was Muhammad's son in law but Muhammad's daughter Fatimah was his progeny. Ali and Fatimah had two sons. To cut the explanation short, the Shi'i view has a line of esoteric intiation through the Progeny.
The two main forms of Shi'ism are Ithna Ashari (Twelver) and Ismaili (main form being Nizari).
Shi'ism doesn't place as much emphasis on fiqh in comparison to Sunnism but it's primary school is known as Usuli, which is based around a more rationalistic exegesis in order to derive legal rulings.
Both Shi'ism and Sunnism have different Hadith collections but share the same Qur'an. Sunni and Shi'i Hadiths often do overlap but chains of narrators are different, etc.
As for Sufism, it's not a 'sect' or a 'branch', it's a practice within Islam - properly known as Tasawwuf. Most Sufis are Sunnis, but there are a few Shi'ite Sufi orders (called Tariqas).
Sufism is a tradition of initiation claiming to go through Ali (who I mentioned), so there is a distinct understanding of esotericism in Islam tied to Ali.
Sufism is often wrongly described as "mysticism". While it does contain some mystical practices in many Tariqas, it remains an esoteric practice. It's hard to really describe other than that it understands the Qur'an in the most deepest ways. Like everyone else, Sufis strongly adhere to the Sharia (and it's inner realities).
As for Wahhabis and Salafis, they are strands that are often associated with 'fundamentalism' within Sunnism. They are basically the only true reform movements in Islam but they are also the cause of much of terrorism (oh the irony!
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Both of these strands of thought overlap, they tend to have quite an emphasis on the "heretical" (to borrow the non-native term) scholar (who was lauded and heavily opposed by the orthodox at the time) Ibn Tamiyyah, alongside this there tends to be a strong emphasis on the notion of the Salaf (basically the generations after Muhammad himself) as being the 'true embodiment of Islam'. Basically those reformists take quite heavily towards what is dubed Takfirism (excommunication) where they often declare fellow Muslims as being kafir etc. Yes it's a mess, yes they get a lot of attention by everyone who is ignorant to everything Islamic, yes it's a pain in the arse.
This is a basic but comprehensive break-down.
And for those reading, no there are no similarities between the "Protestant/Catholic" split and Sunnism/Shi'ism, they are typologically unrelated and therefore completely inapplicable comparisons.
The only comparison in Christianity that I can give that mirrors the Sunni/Shi'i thing, would be the conflict between James (author of that epistle) and Paul. Except for, it'd be like if James' religion wasn't buried in the dust of history by Paul's
- and if Paulian and Jamesian Christianity both lived for 1500 years for the most part alongside each other mostly in good standing with each other, defining each other by their commonalities rather than differences.