The former deputy director of the CIA regards the group as potentially more threatening than ISIS. The Pentagon says the group was "nearing the execution phase" of an attack on the U.S. or Europe. And an expert on al Qaeda says they are "following bin Laden's vision."

The group is called Khorasan, a collection of al Qaeda veterans who fought in Afghanistan and Pakistan. And while ISIS has been grabbing most of the terror-related headlines in recent months, it is Khorasan that poses potentially more of a threat to the U.S. - which is why it was also targeted by American bombs in Syria on Tuesday.

Lt. Gen. William Mayville, who directs operations for the Joint Chiefs of Staff, said the Khorasan Group was nearing "the execution phase of an attack either in Europe or the homeland."

The general added that it was too early to describe the effects of the eight air strikes against Khorasan. It's unclear whether the group's leader, Muhsin al-Fadhli, or other top operatives were killed. The State Department offered $7 million for information about al-Fadhli in 2012.

Taking advantage of the lawlessness inside Syria, Khorason has been working on new hard-to-detect bombs that can be smuggled aboard airplanes, CBS News correspondent Bob Orr reports.

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Al Qaeda has experimented with non-metallic bombs that may be hidden in shoes, clothing, cell phones, laptops and tubes of toothpaste, Orr reports. That intelligence prompted the TSA in July to tighten security for U.S. bound flights from two dozen foreign airports.

Katherine Zimmerman, a senior analyst at American Enterprise Institute and expert on al Qaeda, says Khorasan is "following bin Laden's vision" and al-Fadhli was one of the few in the terror cell who had knowledge of the 9/11 attacks before they were carried out.

"He is what I consider to be a core al Qaeda member," Zimmerman told CBS News. "He was within that inner circle."

U.S. officials told CBS News that Khorasan is a unit with a mandate directly from al Qaeda's central command in Pakistan, sent into Syria with bomb-making experts from the terror network's affiliate in Yemen, to try and plot attacks against the U.S. and Western allies.

"I think it's important that the fight against ISIS has now gone to Syria," Mike Morell, former deputy director of the CIA, said Tuesday, "but I think it's even more important that we struck the Khorasan group last night."

Morell, who is now a CBS News contributor, noted on "CBS This Morning" that CENTCOM had said it was attacking Khorasan to due to "imminent threat plotting" by the group.

"That's what we were trying to disrupt," Morell said. "What that means to me as an intelligence officer, it means that we had detailed intelligence on attack plotting, either in the United States, or in Western Europe, or in both."

As for why al Qaeda has deployed a group to try and recreate in some fashion their Sept. 11 plot, Morell said the group sees the aviation industry "as a symbol of the West."

In addition, "they believe if they damage the airlines they can damage the American economy, as we saw with 9/11," Morell said, adding that the terror network is also likely still of the mind that what worked once can work again.

What makes Khorasan so dangerous -- given its presumed access to the pool of hundreds of U.S. and European jihadists who have flooded into Syria to join the fight -- is the group's suspected members from or trained by al Qaeda's branch in Yemen, AQAP.

AQAP has been considered for years one of the most direct and imminent threats to the U.S., boasting al Qaeda's master bomb-builder, Ibrahim al-Asiri.

"That is very worrisome because that brings together two pieces of a potential plot in the West," said Morell. "It brings together Western fighters who have gone to Syria to fight -- so capable of carrying out operations in the West -- with this bomb technology that Asiri brings to the table. You put those things together, you have a serious threat."

Khorasan does not function as an independent group on the Syrian battlefield. It is part of or at least directly linked to al Qaeda's franchise in the country, known as the al-Nusra Front, and as CBS News correspondent Clarissa Ward reports, attacking it may bring repercussions.

Unlike the attacks on ISIS, "airstrikes against Nusra are not likely to be very popular on the ground," Ward said on "CBS This Morning."

"Although both espouse the same extremist ideology, Nusra has large support among the Syrian population, and has actually been fighting against ISIS on the battlefield -- at times even alongside the Western-backed, so-called 'moderate' rebels that the U.S. is hoping will fight this war," explained Ward.

She said American strikes against al-Nusra could "put those U.S.-backed fighters in a very tough situation, because they simply do not have the weaponry or the manpower to fight the Assad regime and ISIS, and now potentially the Nusra Front as well, at the same time."

The U.S. State Department made it clear that as far as the Obama administration is concerned at least, a strike on Khorasan is not the same as a strike on al-Nusra.

CBS News correspondent Margaret Brennan reported that, according to State Department officials, there is "some" overlap between al-Nusra and Khorasan, but they are not one in the same.

A Department official told Brennan that Khorasan refers to a network of al-Nusra Front and al Qaeda extremists and their associates who share a history of training operatives, facilitating fighters and money, and planning attacks against U.S. and Western targets.

Early Tuesday, Syrian activists said airstrikes overnight had killed as many as 50 al-Nusra fighters in rural Idlib province, which lies to the west of Aleppo. It remains unclear who carried out the strikes -- with some witnesses saying they were U.S. missiles and others saying it was Syria's own military, on the orders of President Bashar Assad.