Salafis share a method and divide over what follows from it. The most used map of the divisions comes from Quintan Wiktorowicz, and it is worth knowing both what it explains and where it fails.
The shared method
All Salafis hold that the first three generations of Muslims understood Islam correctly and that everything added since must be tested against them. That produces a shared commitment to the literal reading of the Quran and the hadith, a rejection of the four schools of law as binding, and a hostility to shrine visitation, intercession through saints and theological speculation.
Three postures
Wiktorowicz separates purists, who hold that politics corrupts and that the work is teaching and purification; politicos, who hold that the method must be applied to political questions and who organise accordingly; and jihadis, who hold that violence against rulers and their backers is a present obligation. The three read the same texts and disagree about the analysis of the present situation rather than about the sources.
Where the map breaks
The categories are not stable, individuals cross between them, and the boundaries move with events. The typology also encourages the mistake of reading the third group as the natural end of the first, which the great majority of Salafis reject and preach against. Governments have used the grid to justify treating quietist teaching as a pipeline, and researchers who have tested that claim find the picture far less linear than the policy assumes.