Есть маленький фокус. В масштабах пропаганды и количестве лжи.

militant имеет нейтральный окрас. Боевик — нормальное прозвище для чуваков с оружием.

However, the current meaning of militant does not usually refer to a registered soldier: it can be anyone who subscribes to the idea of using vigorous, sometimes extreme, activity to achieve an objective, usually political. For example, a «militant [political] activist» would be expected to be more confrontational and aggressive than an activist not described as militant.

Rebel

This word is far more common in the corpus! Just in the period of 2000-2006, it was applied to groups in Burma, Sri Lanka, the Philippines, Sierra Leone, Ethiopia, Colombia, Myanmar (Burma), Macedonia, and Afghanistan.

Notice already that there is no overlap between these places and those where Time writers talk about “separatists.”

Militant

Today, this word has been applied to Hamas, Al Qaeda, and other radical Islamist organizations, as well as groups in Saudi Arabia, Iraq, Turkey, and Pakistan. (Do you notice a geographical pattern here?) However, in the 1960s and 1970s, it was mostly used in reference to the militant black movement (a branch of the civil rights movement), but there were also militants in New Mexico, Puerto Rico, India, and elsewhere. The IRA in Ireland is also described here as a militant group (I think we would get a different result if we searched a British/Irish corpus).