With the recent spate of horrific attacks from Nice to Dhaka, and political rhetoric around Islam and Muslims becoming more heated, divisive, and sloppy, it’s become increasingly important to at least define our terms. The words “Islamism,” “Salafism,” and “jihadism” are tossed around and lumped together all too often. Though we recognize this list isn’t exhaustive, here is a brief cheat sheet on the distinctions between three contemporary—and sometimes confusing—movements in Islam that dominate our headlines, and will likely dominate them for some time to come.

Islamism: Islamism as a phenomenon incorporates a wide spectrum of behavior and belief. In the broadest sense, Islamist groups believe Islamic law or Islamic values should play a central role in public life. They feel Islam has things to say about how politics should be conducted, how the law should be applied, and how other people—not just themselves—should conduct themselves morally.

To be or become an Islamist, however, is a conscious act of political affirmation. As the Princeton historian Michael Cook writes, Islamists are “at pains to construe their politics out of their Islamic heritage.” This also explains, in part, why Islamism isn’t just a reaction to modernity, but a product of it. In the pre-modern era, Islam imbued every aspect of public life, providing an overarching religious, legal, and moral culture. It went without saying, so it wasn’t said. With the advent of modernity, Islam, for the first time, became a distinct political project.

But why not treat Islamists as we would treat any other ideology or political platform? For starters, modern liberal sensibilities shy away from enshrining a privileged position to any one religion, out of fear of placing constraints on individual freedom—yet the point of Islamism is to advocate for a privileged social and political role for Islamic belief. How each Islamist group goes about promoting Islam and Islamic values differs widely from group to group given their local circumstances.

The definition above is broad enough to capture Islamism’s basic impulse, but this broadness also means that the category includes both extremist groups like ISIS that use violence and terror and mainstream parties like Tunisia’s Ennahda (which is one reason Ennahda has recently distanced itself from the term). This diversity in the Islamist experience is why it’s important—and, from a national security standpoint, perhaps more important ever—to make careful distinctions between Islamists. While extremists may garner the most attention, the vast majority of Islamists are not, in fact, violent.

Mainstream Islamism: Mainstream Islamist groups primarily consist of Muslim Brotherhood and Brotherhood-inspired movements. Their distinguishing features are their gradualism (historically eschewing revolution), an embrace of parliamentary politics, and a willingness to work within existing state structures, even secular ones. As Hamid discusses in his new book, Islamic Exceptionalism: How the Struggle Over Islam is Reshaping the World, mainstream Islamists, contrary to popular imagination, do not harken back to seventh century Arabia.

The basic project of mainstream Islamism, if it can be summed up in a sentence, is to reconcile pre-modern Islamic law with the modern nation-state. In many ways—and perhaps the most important ways—the state has gotten the better end of the deal. The very process of modern state-building—and the state-centric international environment which facilitated that process—has had an inherently secularizing effect on social and political institutions. This places pressure on Islamists to limit their religiously-motivated ambitions to a degree that would be unthinkable in the pre-modern past, introducing a substantial degree of tension within Muslim-majority societies that are still largely religious and conservative. What, then, does an Islamist future look like? What exactly are they fighting for? That answer, too, can differ widely depending on which Islamists you talk to.

Salafism: Salafism is the idea that the most authentic and true Islam is found in the lived example of the early, righteous generations of Muslims, known as the Salaf, who were closest in both time and proximity to the Prophet Muhammad. Salafis—often described as “ultraconservatives”—believe not just in the “spirit” but in the “letter” of the law, which is what sets them apart from their mainstream counterparts. In the Arab world today, Salafis are known for trying to imitate the particular habits of the first Muslims, such as dressing like the Prophet (by cuffing their trousers at ankle-length) or brushing their teeth like the Prophet (with a natural teeth cleaning twig called a miswak).

Broadly-speaking, Salafists are less inclined towards active political engagement à la mainstream Islamists, preferring instead a “quietist” approach of preaching, religious education, and avoiding confrontation with state authorities. Some Salafis (in Kuwait and Egypt in particular) have engaged in electoral politics and even formed political parties, although they tend to focus on lobbying for specific shariah-based policies, rather than building big-tent, mass parties seeking executive power. A minority of Salafis are Salafi-jihadists (see below).

Jihadism: Jihadism is driven by the idea that jihad (religiously-sanctioned warfare) is an individual obligation (fard ‘ayn) incumbent upon all Muslims, rather than a collective obligation carried out by legitimate representatives of the Muslim community (fard kifaya), as it was traditionally understood in the pre-modern era. They are able to do this by arguing that Muslim leaders today are illegitimate and do not command the authority to ordain justified violence. In the absence of such authority, they argue, every able-bodied Muslim should take up the mantle of jihad. Contrast this state of affairs with World War I, when the Kaiser himself had to sweet talk the Ottoman caliphate into declaring jihad against the Allied Powers.

Furthermore, the vast majority of Islamic scholars acknowledge that the Quranic verses dealing with violence and the use of force were tied to a specific set of circumstances, and it was the task of clerics to consider when war was or wasn’t justified and how it should be waged. This is the jurisprudence of jihad. Freed from context and the classical rules of warfare, modern jihadist groups generally aim to incite their coreligionists to rise up and fight the enemy en masse, wherever they happen to be and by any means necessary. Theologically, Muslims of various persuasions have engaged in jihad—not just ultraconservative Salafis, but mystical Sufis as well.

Salafi-Jihadism: This is an approach to jihadism that is coupled with an adherence to Salafism. Salafi-jihadists tend to emphasize the military exploits of the Salaf (the early generations of Muslims) to give their violence an even more immediate divine imperative. Most jihadist groups today can be classified as Salafi-jihadists, including al-Qaida and ISIS. Given their exclusivist view that their approach to Islam is the only authentic one, Salafi-jihadists often justify violence against other Muslims, including non-combatants, by recourse to takfir, or the excommunication of fellow Muslims. For these groups, if Muslims have been deemed to be apostates, then violence against them is licit.

Groups like ISIS largely disregard the varied development of Islamic law that occurred over the course of more than twelve centuries, dipping into shariah to provide justification for their project, while ignoring its precepts when the law seems to bind them. And as Salafis, they don’t consider themselves bound to the classical tradition. ISIS and its ilk reject the rich and diverse tradition of Islamic scholarship as filled with sinful “innovations.” In their mind, authenticity lies in reverting to what they depict as Islam’s “original mandates.” Tradition is a fundamentally conservative force. Without it, almost anything is possible.

All in all, terms matter, and if we’re sloppy with our language, politicians may end up pursuing policies that could potentially alienate Muslims across the globe—a quarter of the world’s population. An example of such confused thinking is the bizarre notion of “banning shariah.” (Republican politician Newt Gingrich apparently wants all Muslim Americans to be “tested” and to be deported if “they believe in shariah.”) If decision makers are interested in crafting effective policy when it comes to Islam and Muslims, educating themselves in even the most basic distinctions can go a long way.