“We will not be sending U.S. troops back into combat in Iraq.” – President Obama, June 13, 2014

“As I have said before, these American forces [in Iraq] will not have a combat mission.” – President Obama, Sept. 10, 2014

About 3,300 U.S. troops are now stationed in Iraq, where they are helping local forces battle the extremist group. Over both Iraq and Syria, U.S. planes have been flying bombing and surveillance missions for over a year.

In keeping with Obama’s promises to keep U.S. troops out of another prolonged ground war in the Middle East, the Pentagon has given American troops a limited mission in Iraq, consisting primarily of advising local forces and rebuilding the country’s hollowed-out army. While U.S. forces are not confined to bases, officials say, their mission is very different from that of the 2003-11 war, when U.S. troops fought — often house by house — to end a powerful insurgency.

But depicting the U.S. mission in Iraq became an even more delicate activity last week after a joint raid in the Iraqi city of Hawijah, which freed about 70 Islamic State hostages and left a U.S. Delta Force soldier dead. The death of Master Sgt. Joshua L. Wheeler was the first time a U.S. servicemember had been killed in a firefight there since U.S. troops returned to Iraq last year.

Briefing reporters hours after the raid took place,  Pentagon press secretary Peter Cook said that “U.S. forces are not in a combat role in Iraq.” He said a team of elite U.S. soldiers had provided transport and support for the Iraqi Kurdish commandos. But the Americans were not intending to take part in the raid itself, he said. That changed when a firefight erupted and Wheeler jumped in to help. Later that day, Cook said that Wheeler’s death was the first combat casualty there since 2011.

On Monday, asked about operations in Iraq, White House press secretary Josh Earnest declined to characterize the operations there as combat. He said the “train, advise and assist” mission differed from “the long-term, sustained ground combat operations” that took place after the 2003 invasion. Over 160,000 U.S. troops were stationed in Iraq at the peak of that war.

American officials appear more ready to acknowledge that the flights over Iraq and Syria are combat operations. Not so when it comes to ground operations, perhaps in keeping with Obama’s own statements.

But on Wednesday, Col. Steve Warren, a U.S. military spokesman in Baghdad, described the mission in blunt terms. “We’re in combat,” he said, speaking via video feed to reporters at the Pentagon. “That’s why we all carry guns.  That’s why we all get combat patches when we leave here. That’s why we all receive imminent danger pay. So, of course it’s combat.”

Officials say the ground mission is primarily an advisory, not combat, one, but say American personnel are bound to encounter combat or kinetic situations from time to time, as they did in Hawijah. How often that occurs may depend on whether Obama approves proposed steps that would expand U.S. operations in Iraq and Syria, including embedding American troops with Iraqi units closer to the front lines.

No matter what they’re called, U.S. operations in Iraq are unlikely to resemble the scale and scope of the last Iraq war anytime soon. “There’s been an awful lot of energy around making rhetorical hay out of a few of these words,” Warren said.

It’s hard to sum up the situation on the ground in Iraq in a way that would fit on a “reasonably sized bumper sticker,” Earnest told reporters. “But I do think it is important for people to understand precisely exactly what our men and women are doing inside of Iraq,” he said.

Officials have not provided a detailed account of what all American forces, especially Special Operations forces, are doing in Iraq.

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