In September, al-Qaeda told ISIS its leader couldn't run a Caliphate. In October, ISIS fired back: "Your boss is senile ... and you are a bunch of donkeys." The two groups, vying for leadership of global jihad, seem to have taken a page out of the playground playbook.

"They've had a war of words for several years now, but it has really intensified," says Patrick Skinner, director of special projects at the Soufan Group and a former CIA case officer. Some of the exchanges seem almost childish. "Al-Qaeda is trying to play up that notion that ISIS is the spoiled brat."

The most recent tit-for-tat may have begun this summer when, as The Daily Beast reported, late al-Qaeda spokesman Adam Gadahn scolded ISIS for its brutality. He reminded the group of the dire consequences of its actions, and, as if wagging a finger, told ISIS "No paradise for you!"

In August, when it was revealed that longtime Taliban leader Mullah Omar had been dead for two years, ISIS officially mocked al-Qaeda's leader Ayman al-Zawahiri, who had been maintaining the fiction of his personal allegiance to the dead man. "ISIS had a field day with that," says Skinner.

And in October, ISIS released an audio message that, amid threats aimed at Russia and the United States, challenged the al-Qaeda leadership to consider why so many militants have sworn allegiance to ISIS. It also amplified its signature threat to anihilate those who do not join the ISIS ranks.

Patrick Skinner notes that official ISIS statements tend to mirror what supporters say online. "They dominate Twitter because Twitter is perfect for snark. And Islamic State kind of embraces that."

"Al-Qaeda tries to pivot that back," Skinner notes. "Al-Qaeda adopts a condescending tone, as if to say 'Look what ISIS is doing. Now please stop.' But [Al-Qaeda] never threatens ISIS."

Despite their different approaches, and their growing antipathy, the two groups are not that far apart politically. "ISIS and al-Qaeda share the exact same ideology," observes Skinner. "They share bin Ladenism. It's just a matter of style and allegiance that divides them."