It is very difficult to grasp an overall picture of variations in Islam, unless you develop an understanding of the broader categorizations and their usual points of dissent. For example (in a rough chronological order of prominence)
Political Theory
The tensions in the early Muslim society "crystallized" as political schisms, but all political tensions don't arise in vacuum. We can identify several sources of tensions leading up to the proliferation of partisanships: tribal frictions, changing dynamics of empire, power struggles, interpretation of scriptures, interpretation of history among possible others.
Shia/Non-Shia (note I didn't use Sunni) dichotomy crystallized as political dissent (not to be understood as a characterization of Shia Madhab) but it went on to embrace all other categories. Almost all divisions within Shiism are mainly of political nature with doctrinal underpinnings, like the Zaidis, Ismailis, Twelvers and so on.
Khawarij and the modern-day terrorists arguably also belong to this category due to their abuse of political theory.
The usual points of dissent in this category are the succession of power, and matters relevant to the establishment of political authority like Imamat and Caliphate - in short the whole sphere of political theory.
Theology/Philosophy
Maturidi, Asha'ri are examples from this category. Mutazilla are the most famous (especially in Western discourses) symbolizing rationalistic spirit of Islam. Almost all Hanafis are Maturidis in theology but many are oblivious to the fact. The usual points of differences are the Unicity of God, His attributes, free-will vs. fate etc.
I'm not sure whether the philosophers (not theologians) can form a separate sect simply because of scarcity. The point of contention for the philosophers was the tension between reason (intellect) and revelation. We have independent names here like Alkindi, Avicenna, Alfarabius, Averroe, Brethren of Purity among others.
Legal Theory (Jurisprudence)
Names like Hanafi, Jaffari, Shaafi etc. known as the schools of law belong to this category. The points of difference are the Usul (principles) of law and the derived law.
Orthodoxy (Sunnism)
The Sunni/Non-Sunni or the Sunni/Salafi dichotomy divides on the basis of right flavor of being a traditionalist (Sunni). The usual points of dissent are servile-imitation (Taqlid), independent reasoning (Ijtihad), organized religion etc.
Mysticism
The whole corpus of Sufic teachings, the Taraiq and Silsilas lie under this category. Sufi emphasis is on the inner meanings of being a Muslim mystic. Points of dissent are ascetic and mystic practices, esoteric interpretations and theology.
Secularism (Modernism)
Neo-Mutazilites and Quranists belong to this category. This is more of a movement towards reconciliation of secular and religious since the mid 19th century onwards. The usual point of dissent are the nature and degree of reforms in all other categories.
NOTE: The first five categories were also paradigm shifts, i.e. they brought about fundamental changes to the basic concepts of religion, and experience of Muslims. They almost serve as vital stats of religious life (not to be confused with sectarianism).
NOTE: The chronology is based only on rising to prominence so as to be easily identifiable, and not on the dates of nascence. Almost every denomination loves to trace their origin back to the first generation of Islam, by hook or by crook (and manages to do so might I add).
The above categorization should only be taken as a tool for analysis, in reality individuals and groups are a complex mix of affinities towards ideologies from these categories. The names that I've put under each category are only based upon the dominant traits of a group and for example, it doesn't mean that a Salafi is only an antonym to Sunni. Salafis in general also oppose Sufis, as a matter of fact, some would even say that Salafis are more an opposite of Sufis than Sunnis.
A great source of confusion is the demarcation between an ideology, a movement and a sect. Certainly, almost all sects were initially pure movements based on ideologies and the solidification point came only when a sizable majority self-identified themselves with a chosen label. However, neither the ideology as pure ideology or movement as pure movement (devoid of sectarianism) ceases to exist after the solidification of a sect. In other words, new sects may appear based on preexisting and shared ideologies in a different socio-political context. The confusion comes when the same name is used to denote a movement, ideology or a sect. The latter three categories are good examples of names that are overloaded with meanings.
There are some divisions that fall outside the periscope of any of the aforementioned categories. The Ummayad era tensions between Arabs and non-Arabs (mawali) culminated centuries later in the pro-Arab Deobandi and pro-Ajam Barelwi factions. Both are Sunni cum Sufi cum Hanafi cum Maturidi but differ on affinities towards Arabs, a spirit inculcated by the very founders of seminaries at Deoband and Bareli. Present day controversies between them are subsequent, apparent and of peripheral yet divisive nature.
The diagram http://www.informationisbeautiful.net/visualizations/islamic-sects-schools-branches-movements/ provides a convenient way of looking at the divisions. However, the only way for me to make sense of the graph is to think of the diagram as depicting the divisions on the basis of "Popular Perception" only.
Even https://en.wikipedia.org/wiki/File:Islam_branches_and_schools.svg has factual errors like listing Ahmadis as Muslims without qualification. It depicts Druze as controversial and if that is the case then the Ahmaddis should also be mentioned as such. Some names mentioned earlier are absent, possibly either because they were deemed as out-of-scope or non-contemporary.
