Even as the terrorist incident in Nairobi enters its fourth-day there is still a massive amount of confusion about who, precisely, is responsible for attack. There have been numerous claims from Kenyan officials and local terror group — with different spokespeople for both groups occasionally contradicting each other. So what exactly is everyone saying?

To begin with, it's clear that the main impetus for the attack is coming from Somalia, where a group known as al-Shabab has done battle with the local government and the Kenyan military for year. The attack is meant to be retaliation for Kenya's involvement in the Somali conflict, which Kenya claims is for their own security. However, there is some question about whether al-Shabab is capable of orchestrating such an attack given the heavy losses the group has sustained in recent years.

On Tuesday, Kenya's foreign minister claimed it was al-Qaeda, not al-Shabab that was responsible. However, this may simply be a matter of semantics. In 2012, al-Shabab and al-Qaeda announced that they were forming an alliance "in a single conflict against an international Christian crusade" and they were essentially partners. A "commander" in al-Shabab even told Al Jazeera that "Al-Qaeda are our leaders, they are our mentors." So in practical terms, it seems there really is no difference between the two groups, aside from the name and location.

Who actually planned the attack and supplied the fighters may be a different story, however. Al-Shabab has traditionally concentrated their efforts within Somalia, and despite recruiting heavily from those living in foreign countries, they have a reputation for being hostile to outsiders. An American-born jihadi known as Omar Hammami who had joined forces with al-Shabab, was recently killed by that same group, after an internal conflict with the leadership. The rift allegedly came about because of al-Shabab's attitude toward non-Somalis and their reluctance to carry the fight beyond their borders. 

So that makes the claims that several of the attackers were American or British citizens, even more confusing. From the very beginning of the attack, there were witnesses reports that Westerners were involved in the attack, and Kenyan officials continue to insist that "two or three Americans" and one British citizen, all of Somali or Arab origin, were among the gunmen. There were even unconfirmed reports that a white woman, possibly a British woman named Samantha Lewthwaite, was not only participating, but was even giving orders during the assault. Lewthwaite, who is wanted by Kenyan police for ties to other terror plots, is known as "the White Widow" in intelligence circles, because her husband was one of the suicide bombers who took part in the July 7, 2005, subway attacks in London.

However, al-Shabab themselves shot down those claims on Tuesday, saying "Those who describe the attackers as Americans and British are people who do not know what is going on in Westgate building." That also contradicts earlier claims made by an al-Shabab Twitter account that has since been shut down. So who is really speaking for al-Shabab? Are the Kenyans wrong? Is al-Shabab unwilling to admit they had outside help? Is al-Qaeda relying on Western partners, or giving orders to its local affiliates? Or is just more semantics designed to keep further the legend of al-Shabab's strength?

Until the perpetrators are all rounded up and identified, there's no way to know for sure. Even then, it's likely that these questions will remain. Even if the motives are obvious, the true planners of the attack may never be known. But no matter the outcome, the incident has surely drawn Kenya even deeper into the fight against terrorism.